The 4th-level cleric spell Olidammara's bard spell [trans] (Dragon #342 (Apr. 2006) 42), in part, says
Casting this spell allows you to prepare and cast a limited number of bard spells as if they were cleric spells. Each casting of Olidammara's bard spell lets you prepare up to three levels of Bard spells (these cannot be combined to prepare Bard spells higher than 3rd level). A cantrip counts as 1/2 level for this purpose. You may spontaneously convert these prepared Bard spells to cure or inflict spells just as you would any other non-domain spells. These spells are considered divine spells. You use your Wisdom modifier for the DC instead of your Charisma modifier. These Bard spells always have a verbal component (either singing or music) just like an actual Bard spell. If the bard spell has a material component or XP cost, you must pay that cost when you cast the spell.
(Emphasis mine.) The heart of the disconnect seems to be whether the reader views the first sentence as introducing the topic of preparing and casting the bard spells or the reader views the first sentence as beginning the explanation of how to prepare and cast the bard spells.
Is the first sentence an introduction?
I suspect that it probably is, but it makes the spell worse. If the first sentence introduces the topic, then it's the second sentence that explains how that topic is handled. Thus that first sentence is essentially saying I'm going to tell you what I'm gonna tell you about, but it's that second sentence that explains how to actually go about performing the task the introduction describes. (Honestly, this isn't a particularly dumb way to do this; it's a relatively common discourse pattern, really.)
In other words, this reading would have the cleric would cast the Olidammara's bard spell spell while she's preparing her other cleric spells then—while still preparing her spells—prepare in empty cleric spell slots the picked number of effective levels of bard spells in the appropriate and corresponding empty cleric spell slots.1 (A player can cross off the bard spell spell from her cleric spells prepared and write down the bard spells prepared instead of her normal cleric spells. Done.)
I imagine that this is a common reading of the spell. It's not challenging to read it this way, and after reading it that way myself, I find it hard to go back to the reading below. However, in addition to this reading being incredibly conservative—spending a 3rd-level spell and a 4th-level spell on a 3rd-level spell is rarely a good trade—, this reading leads makes a wand of Olidamara's bard just a fancy stick for those who lack cleric casting.
Is the first sentence rules?
Taking its cue from the 4th-level Wiz spell Rary's mnemonic enhancer [trans] (PH 268), the Olidammara's bard spell spell provides the caster the ability to prepare and cast the spells beyond those the caster could normally prepare and cast.2 The spell itself grants these abilities to any and all who cast it. While the caster must still prepare the bard spells at the same time as any cleric spells she prepares, the prepared bard spells don't count toward any other limits except, probably, the spell's own (i.e. casting the spell multiple times may not yield multiple batches of bard à la cleric spells). Even better, if the caster of the Olidammara's bard spell is a noncleric, then the creature "chooses a particular part of the day to pray and receive spells" (PH 179 and here) which, conveniently, may be right now.
This reading makes the Olidammara's bard spell spell much more interesting, and a wand of Olidammara's bard spell becomes an incredibly versatile noncombat problem-solving tool in the hands of a creature without cleric casting and with decent ranks in the skill Use Magic Device and who's an ally of well-informed bards.
Which is better for the game?
If the DM is worried about the spell unbalancing the campaign, the DM shouldn't allow the spell into the campaign. That said, using the spell the first way is a safer move if the DM's worried that the spell may cause problems but not excessively worried. On the other hand, a DM who's acclimated to the wide variety of kooky stuff that a 3.5 PC can bring to the table probably won't even question a PC that's using the Olidammara's bard spell spell the second way.
Also, ask the DM if any cleric can cast Olidammara's bard spell
The Olidammara's bard spell spell has the entry Level: Cleric 4 (Olidammara), but this doesn't automatically make the spell exclusive to clerics of Olidammara or to those that possess the feat Initiate of Olidammara (Dragon #342 51–2). In fact, that parenthetical notation meant at first only that the spell originated among Olidammara's followers. Magic of Faerûn (Aug. 2001) on Origins says
Some spells have an origin given in parentheses after the spell’s level. This indicates the deity that initially provided this spell…, a group of spellcasters that created the spell…, or a region where the spell originated…. Since these spells have been created, others have duplicated the efforts of the creators…. (68)
So, really, anyone who had such spells on their class's spell list could cast them, and the spell's origin was flavor text. However, the Player's Guide to Faerûn (Mar. 2004) says, "If you use initiate feats in your game, you should not allow clerics without the appropriate initiate feat to cast those spells" that have an origin (79). Ask if the DM's following the Player's Guide's recommendation… and if any of this applies to the Greyhawk initiate feats.
1 I don't think I've ever seen a PC to cast a spell while preparing his spells. I don't think I'd have a problem with it as a DM, but if a DM does, then the bard spell spell can be prepared the previous day and cast right before preparing spells the next day. That sounds, like, super annoying, though.
2 Before reading the enhancer spell, I'd thought the author of the bard spell spell might've deliberately omitted mentioning spell slots, but Rary's mnemonic enhancer uses the same kind of language as the bard spell spell, so unless the DM wants to call shenanigans on both spells, I'd not worry about spell slots.