Ken Levine announced during E3 2011 that Irrational Games were developing a BioShock game for the PlayStation Vita, but since then, there has been very little information shared about it.
This lack of information had led to fears that the game would end up being swept under the carpet, but this has been rebuffed by Ken Levine.
When responding to a fan on Twitter, Ken Levine (who's the the Creative Director at Irrational Games) said he talked to both Sony Computer Entertainment and 2K Games about the project just yesterday, suggesting that it's very much still alive.
Outside of this, Levine offered no new information, so at this point we don't even know if BioShock on the PS Vita will be related to either the original BioShock or BioShock Infinite.
This is the kind of game the PS Vita could really use, with the console still struggling to appeal to the mass market.