The feature you describe is overpowered. The arcanist class, wholesale, is pretty much overpowered. While 3.5e can definitely manage such things, too, they require a lot more jumping through hoops and combos; they didn’t just print stuff that high-power for the most part.
For the best “they just printed it like that,” there are:
Psionics (Expanded Psionics Handbook and/or Complete Psionic)
(Since the SRD includes Expanded Psionics Handbook, I have linked to everything from that book. Everything in this section without a link—ardent, Practiced Manifester, dimension hop—is found in Complete Psionic.)
Psionics has a minor “thing” for tactical teleportation, and tends to be a little more efficient about it than spellcasting. For example, the 3rd-level psychic warrior power dimension slide can teleport anywhere in close range for 5 power points (equivalent to a 3rd-level spell slot, sorta), and it can become a move action for 9 power points total (equivalent to a 5th-level spell slot, even more kinda-sorta).
Note that psychic warriors don’t get 3rd-level powers until 7th level (but can manage the 9-pp version at 9th)—you can shave one level off of this with war mind, or four levels by using ardent with Practiced Manifester and Expanded Knowledge. In all cases, some of those levels can be replaced with cerebremancer to limit how much spellcasting it costs (to a minimum of 2 ardent levels, as in sha’ir 3rd/ardent 2nd/cerebremancer 3rd with Practiced Manifester and Expanded Knowledge).
There is also dimension hop, which is a 1st-level ardent power and a swift action too, but since only teleports 10 feet + 5 feet per power point, you need to spend 11 power points (and therefore need to have ML 11th) in order to get the 60 feet you want. Ultimately, dimension slide just costs less in both cerebremancer levels and power points (by 2 in both cases, coincidentally), making the feat in Expanded Knowledge probably worth it.
On the other hand, the class level thing may be kind of moot since with only 5 effective ardent levels in ardent 2nd/cerebremancer 3rd, your power points per day could be as little as 34, assuming the minimum Wis 14 (which is probably safe to assume for a sha’ir). That only allows 3 manifestations of an augmented dimension slide, not proper spamming. More cerebremancer levels will dramatically increase that number, however. (Reluctantly, I’ll also point out the pure cheese at the bottom of this answer that’ll make it so you don’t really have to worry about power points at all.)
And in any event, you’re not going to advance ardent manifesting enough to achieve 9th-level spells in two different classes with this anyway, so you’ll probably want to just go with more cerebremancer to get 9th-level spells and 9th-level powers.
Flicker, in wand form or via noctumancer (Tome of Magic)
Flicker is a 3rd-level shadowcaster mystery, which means you can get it in a wand. It’s a standard action to turn it on, but then for the next 1 round/level, you can teleport 5 feet per 2 caster levels as an immediate action. For a shadowcaster, this is fine—the shadowcaster is a terrible class—but allowing wizards and the like to get it just via a wand should, like abrupt jaunt, be banned. Note that you can cast flicker itself as a swift action by using Quicken Mystery, which could be applied (probably) to the wand with the Metamagic Spell Trigger feat from Complete Mage. You’ll also need Use Magic Device, at least 1 rank to use it at all, and enough bonuses (from ranks or otherwise) to routinely hit DC 20.
Noctumancer (the arcane/shadowcasting equivalent of mystic theurge) is enterable while retaining 9th-level prepared arcane spells, so you could potentially access flicker “fairly” while keeping to your goals. This saves a ton in gold since you’ll want the caster level to move farther, which noctumancer gives you “free” but costs quite a lot in a wand. It also means you could use a lesser metashadow rod of quicken mystery instead of Metamagic Spell Trigger, which is probably a good trade.
Unlike most theurge classes, noctumancer avoids the “what next?” problem because you can also advance shadowcaster with mystic theurge. The ideal build, assuming you want to maximize flicker caster level, is probably sha’ir 1st/shadowcaster 3rd/noctumancer 10th/mystic theurge 6th (you can get in with sha’ir 1st using Precocious Apprentice—note that you can arguably use Precocious Apprentice on shadowcaster, instead, so you could start as shadowcaster 1st/sha’ir 3rd to maximize your sha’ir spellcasting).
There is also an argument that a greater shroud of night could qualify you for casting 2nd-level mysteries, since the item “can also cast the mysteries dancing shadows and shadow skin each once per day,” and those are a 3rd-level and 2nd-level mystery, respectively. This is a huge stretch since it is explicitly the item casting these, not you. Note that you’d still want one level in shadowcaster so that noctumancer has something to progress; otherwise the exercise is largely wasted. Since a greater shroud of night is quite expensive, unless you are also breaking the economy, Precocious Apprentice gets you into noctumancer sooner, and if ruled to apply to the shadowcaster, with the same number of lost spellcasting levels, so it’s sort of irrelevant.
Unfortunately, like psionic version above, if you go with noctumancer that will basically become your second class; you’re not getting a third one. That’s unfortunate because, unlike ardent manifesting, shadowcaster mysteries are terrible. They go to 9th level, and they even count as spells kinda, so they meet your goal, but they’re not a good approach to that goal.
Blink shirt, by dipping totemist and optionally taking soulcaster (Magic of Incarnum)
Blink shirt is a totemist soulmeld that enables a 10 ft + 10 ft/essentia teleport at-will as a standard action. You can get it with the Shape Soulmeld feat, but you’ll prefer to dip totemist because it becomes a move action when blink shirt is bound to the totem chakra. The totem chakra is accessed (only) via the class feature of totemist 2nd, so this is a minimum of 2 missed spellcasting levels if you want to make it a move action (which you do).
Essentia investment in any given receptacle, e.g. the blink shirt, is capped at 1–4 based on your character level (1 + ⅙ your level, to be precise), so you’re looking at 20-ft to 50-ft teleports from that alone. However, that same totemist 2nd feature bumps the cap by 1 for whatever you’ve bound to your totem—in this case the blink shirt—and there’s also a feat (Expanded Soulmeld Capacity) and a magic item (incarnum vestments, a type of incarnum focus) that can improve it further by 1 each, so you could be looking at up to 80-ft teleports with all three and sufficient essentia to fill it.
Totemist 2nd also qualifies you for the soulcaster prestige class that will advance both your arcane spellcasting and your meldshaping to ensure you do (as a sha’ir 3rd/totemist 2nd/soulcaster 7th with the required Incarnum Spellshaping feat), though depending on your desires for other prestige classes you might want to use Bonus Essentia, and/or other incarnum feats, to get the necessary essentia in fewer soulcaster levels than that.
Warning: incarnum focus says something about essentia investment being “up to your Constitution bonus.” It’s written as if it’s just reminding you of a default rule, but this isn’t. Still, it may mean that for that 7-essentia, 80-foot blink shirt, you’re gonna need 24 Constitution, which is tricky since it’s hard to find bonuses that stack beyond a +6 enhancement bonus. You could argue that you’re applying the incarnum focus bonus prior to the totem chakra feature or the Expanded Soulmeld Chakra feat, which lowers the requirement to a much more manageable 20 Constitution, but you’ll have to check with your DM on that.
Warning: blink shirt’s teleport is “as dimension door,” so you’re going to want to do it as the last thing on your turn.
Warning: getting dual-9ths alongside totemist 2nd isn’t going to happen, though of course you could just advance totemist itself.
Flicker and blink shirt, probably as a totemist with a wand (Magic of Incarnum and Tome of Magic)
You could combine both of the above, potentially limiting the necessary caster level for flicker and the necessary essentia investment in blink shirt. A totemist 2nd with a CL 6th wand of flicker gets 30 feet from blink shirt and another 15 feet from flicker, as a move action and immediate action respectively, and you don’t need noctumancer or soulcaster at all if you don’t want them. Bonus Essentia will get you up to 50 feet from blink shirt for one feat; another incarnum feat will (at 18th) allow you to max blink shirt out at 5 essentia for 60 feet. Taking levels of shadowcaster, noctumancer, or soulcaster, or taking the Expanded Soulmeld Capacity feat, or buying higher-CL wands of flicker or an incarnum focus, are all also options for expanding your range.
Shadow jaunt, stride, and/or blink, via Martial Study or jade phoenix mage (Tome of Battle)
Shadow jaunt is a 2nd-level Shadow Hand maneuver, meaning it can be accessed with a Martial Study feat starting at 6th level, or bought for 3,000 gp in the form of novice shadow hands gloves. It teleports you 50 feet as a standard action, and can be used once per encounter (or more, if you are actually a martial adept, though it never becomes “spammable”).
The 5th-level shadow stride is the same, except it’s a move action and available without class levels either at 18th level with Martial Study, or with the 15,000-gp scholar shadow hands.
And then there is the 7th-level shadow blink, which is a swift action and available to learn yourself only with (minimum) three levels in an initiating class, though master shadow hands could get it for 45,000 gp. Since those levels could be in jade phoenix mage, which advances spellcasting at all levels except 1st and 6th, this could mean only a single missed spellcasting level.
These are not spammable, and barring an idiot crusader build (which can’t be achieved while also achieving your spellcasting goals), there is no way to make them spammable. The reason it’s worth bringing these up even after the above clearly do better is because 1. these are easier, just requiring a feat or non-consumable item, and
- these are Extraordinary abilities.
That’s why I mention Martial Study and/or class levels even though shadow hands is arguably much cheaper: if your access to these is via a magic item, you lose that access in an antimagic field. If you actually know them yourself, however, you can initiate them even in an antimagic field. The range is “only” 50 feet, and cannot be extended, and you need both line of sight and line of effect to where you want to go, but nonetheless, if you are concerned about teleporting out of harm’s way, these provide a kind of ultimate level of reliability, potentially for as little as a single feat.
Theoretical optimization: no limits of any kind
As for shenanigans, there’s basically no limit. Pun-Pun is possible in 3.5e, after all, and Pun-Pun can teleport any distance he likes, as often as he likes, for any action he likes, including free probably. Achieving infinite spell slots, and reducing metamagic costs, so that one could, say, cast quickened greater teleport every round, is also possible. One could even use a quickened plane shift to leave the battlefield entirely, and go to a fast-time plane where you can get a full night’s rest before returning for your next turn. At these levels of cheese, however, one could also trivially achieve invincibility, so the point is kind of moot.
I will point out a couple of things for psionics, in particular, that are relevant here, though I’d never allow either in my games (XPH vs. CPsi handled the same way as above, links for XPH and not for CPsi):
There are tricks, e.g. this one, that allow you to recharge power points without requiring a full night’s rest. This is what changes the 9-power-point dimension slide into something spammable. This is important because the manifesting of an effective ardent 5th as described above would include rather few power points, particularly with Wisdom not otherwise being a priority. This thread seems to have a good selection of recharge tricks, including one working with incarnum which is also the source of the blink shirt (though you can’t afford ardent 2nd and totemist 2nd to enable both while still getting 9th-level spells), plus various other high-optimization tricks.
Because it’s absurd and plays into the goals you have in mind, be aware that Linked Power, Metapower, and synchronicity could be combined to reduce the cost of dimension slide to 5 power points, and be something you can manifest any time you like once per round without spending an action. Add schism, fission, temporal acceleration, etc., and linked synchronicity can do a lot more than that, up to and including infinite standard actions per round, each freely taken at any point during the round. In other words, synchronicity should be banned, and Linked Power and Metapower deserve a good, hard look, too. Complete Psionic was a terrible, terrible book, as much as I love the ardent.
An aside: shadow pounce
Telflammar shadowlord 4th (Unapproachable East) and the Crinti shadow marauder 5th (Shining South) grant the ability shadow pounce, found nowhere else. Shadow pounce allows you to take a full-attack after any teleportation. With free-action, swift-action, immediate-action, move-action, and standard-action teleportation in this answer, that could get absurd very, very quickly.
However, both prestige classes require a miserable array of feats, and do nothing to progress spellcasting so they’ll cost you 9ths in anything, to say nothing of dual-9ths. Three or more full-attacks per round is damn powerful, particularly since you can teleport around for each one, but it’s not what you were looking for, it’s a different thing entirely. If you decide to switch to this concept, the Telflammar shadowlord requires more feats, the Crinti shadow marauder requires more class levels: pick your poison.