On the Failure of Travel Devotion
The Travel Devotion feat seems like an answer to the problems with Skirmish - swift action to get an extra move action per round for a minute? Fantastic.
However, there is a problem. It's only 1/day, and the only way to get more uses is to be a Cleric.
Why not be a Cleric? Clerics are great! They can even trade out the Travel Domain for Travel Devotion, saving you a feat? They are also just generally awesome and badass!
The problem is, if your alignment changes, or you don't advance the goals of your chosen god, you lose your powers. If you got Travel Devotion from the class, that includes that. If you got it from a feat instead, it drops you back down to 1/day.
Normal Clerics get enough bazaaamph out of their class to make keeping on the straight and narrow worthwhile - but for a dip, is it worth it?
The downside of a cleric dip and travel devotion isn't mechanical - it's the severe roleplaying onus that comes with taking the level.
Some groups don't enforce alignment or that rule. There's also the 'godless' cleric who worships a cause, although fundamentally that doesn't really solve the problem of 'walking the straight and narrow' that alignment restrictions and 'worshiping' entail.
So it depends on your group, but it can be at best a slight change in your character all the way to a roleplaying straitjacket.
Do you have other options, though?
Greater Manyshot specifically allows precision damage on each arrow. Can't use Rapid Shot or TWF with it (it caps to the number of attacks allowed by your BAB), but it's still great.
A Belt of Battle can be used to spend charges to grant extra move actions.
The Hustle psionic power converts a swift action into a move action.
Cyran Gliding Boots turn 5' steps into 10' steps.
An Anklet of Translocation 'moves' you 10' as a swift action - at no point does the text say that teleportation is out of the question. NOTE: THEY ARE VERY, VERY CHEAP. YOU CAN PACK LIKE TWENTY OF THEM. (Note: Due to the MiC magic item stacking/custom creation rules, you can add the effects of an Anklet of Translocation to an Anklet of Translocation, for four uses per day instead of 2. This costs you 3.5k, or, 1.4k + 2.1k(150% markup to add item to item). You can add extra uses for extra lots of 2.1k to that one item, and end up with enough short-range teleportation to skirmish to your heart's content. In addition, the DMG's Custom Magic Item Creation rules specify that 5 uses/day costs the same as at-will activation - under those guidleines, an at-will Anklet of Translocation should cost 3,500gp. Which is a steal, but not broken.)
Similarly the Dimension Hop psionic power can move you as a swift action.
The Sudden Leap 1st level Tiger Claw maneuver allows you to move the distance of a single standing jump check as a swift action - with enough jump, you can hit a horizontal distance of 10'.
The Master's Sparring Dummy from the Arms and Equipment Guide teaches you how to take 10' steps instead of 5' steps, as does a DC 40 tumble check(Oriental Adventures expanded tumble skill entry), or a stance from Tome of Battle (forget which one).
Evasive Reflexes gives you a 5' step instead of an AoO, which can be useful if you can set it up right (have the karmic strike or riposte or robilar's gambit feat(s), trigger an AoO from a foe on your turn, get attacked in melee, cartwheel away, rest of your full attack has skirmish). Plus, looks cool as hell.
Dictum Mortuum's Swift Hunter Handbook
Be Levitating and have someone tow you around on a rope. You can't ride a mount and also get skirmish (WotC haet mongols), but you can be towed. Or even carried. Technically being carried is not the same as being mounted (if it is the same as being mounted, your fighter should be wearing a lot of tiny creatures all with the Mounted Combat feat and Ride).
Slide + 5' Step, or, Greater Slide. Allied spellcasters burning spellslots to enable your skirmish attack? You betcha!
Stuff that will get you 20' of movement for Improved Skirmish
Slimmer pickings here. Travel Devotion(if you dip cleric, pick up Knowledge Devotion and Animal Devotion as well, cloistered cleric style), Hustle, high-pp Dimension Hop, Greater Manyshot, Greater Slide. Aaaand that's about it.
No Dipping, No Magic, No Items!
You're looking at;
A DC 40 Tumble Check (Oriental Adventures)
Greater Manyshot (XPH)
Sudden Leap via the Martial Study feat (ToB: Bo9S)
Travel Devotion feat + lots of crying
Evasive Reflexes + AoO generation
Something funky like being dragged that technically meets the letter of the rules while hilariously undermining them.
Letting go of a climbed wall is a free action, you can make Jump and Tumble checks to not take damage from 10' of fall and land on your feet, and then shoot from there/while falling.
An ally with Fling Ally and a Readied action to hurl you when you yell 'now!' is a source of full-attack skirmish damage.
An ally with a Readied action to haul you via a rope somewhere is a source of full-attack skirmish damage.
Being carried by someone with a readied action to move is arguably a source of full-attack skirmish damage (doesn't really count as a mount, -2 circumstance bonus to ranged attacks for poor footing sounds applicable though).
Being on a boat or other mobile platform (wagon) is arguably a source of full-attack skirmish damage.