That's the one thing I don't really like about owning a PS3 (besides, you know, that whole security breakdown thing... >_>). I just can't seem to find many good games for it, and I've had mine for two years. But I've got a few (probably really obvious) suggestions.
I would suggest to you Borderlands. Really, if you liked Bioshock, you'll probably like Borderlands. In my opinion, it's the real sequel to Bioshock. (They're made by the same company.) The ups are the battle system will feel pretty familiar while being completely different (in a good way.) It's got a cast of incredibly colorful characters that provide the game with a lot of laughs, but the downside is it's not very story-heavy. You get into Borderlands because it's fun to play and because it's funny, not because it's got the awesome atmosphere and story as Bioshock. If you enjoyed the plasmids in Bioshock, chances are you'll enjoy the elemental weapons of Borderlands. You can burn, shock, explode, or even chemically MELT your enemies! (Melting is my personal favorite.) You get your choice of four different characters (catering to the four basic fps play types) with different strengths, weaknesses, and special attacks. And one of the best aspects, in my opinion, is the RPG elements. Your character gets more accurate and does more damage with weapon categories you use more often. The downside to this is that at the very beginning of the game, your shots can miss even when you're aiming directly at the person, especially with weapons like the machine gun, but this problem quickly disappears. Borderlands also fixes one of the major complaints I had with Bioshock, namely that dying cost you nothing. The biggest complaint I have about this game is the ending. I was really disappointed, but that hasn't stopped me from starting a new game plus. I think the best way to summarize Borderlands is to say that it is a game that provides you with a fantastic world if not a fantastic story.
Another game I'd suggest is Infamous. Again, the story and atmosphere isn't really on par with Bioshock (but then again, what is?) but it's a great sandbox style game with an interesting battle system. It's sort of a 3rd person shooter, I think? You shoot lightening out of your hand, it's 3rd person, and you have crosshairs on screen at all times. It's got a set of interesting powers that you can level up as you progress through the game, but like Bioshock it's got one of those morality systems that's all or nothing. Being good or bad leads to the ultimate powers in the game, so you can't pick and choose your choices. It's all or nothing. All in all, it's a fun game that provides a decent challenge (though to be fair, I played for the first time on Hard and I'm not really that great at video games.). There's a lot of collectibles that give you a break from the missions and it's visually pretty good looking. There's a lot of freedom in the way you complete most missions thanks to the city setting. If one approach isn't working, just sneak around the building and take the enemies out from another angle!
But to be completely fair, if Infamous isn't your cup of tea, you might really, really like Prototype instead. Most people are split, really liking one or the other. Personally, I didn't like Prototype at all, so I can't tell you much about it.
Heavy Rain is another that I really liked. Visually, it's beautiful and it's probably got the best storyline of any PS3 game I own. The downside is it's not a typical game. It's basically a game comprised entirely of quicktime events. Which sounds like it would suck, but as far as quick time events go, Heavy Rain provides some of the best examples. Some people can't look past the fact that it's not a typical game, and completely hate it, but if you can give the game a chance, it's really one of the most engaging and powerful stories I've ever seen in a game. It also has the ability to crank up the atmosphere, like Bioshock. Once the story gets going, you really get into it. At least, I did.
If you ever played PS2 games like God of War or Devil May Cry (then obviously you might want to look at their sequels but) I would also suggest Bayonetta. It's another one of those games that's basically all fun battling and insane, nonsensical story. The main character is a Brittish witch with a fondness for nudity and lollipops. It's over the top and all about fan service, but it's got some of the funnest boss battles I've ever played in a game all about action.
If you enjoyed the alternate historical timeline of Bioshock, you might want to pick up Fallout 3. Personally, I find it pretty hard. The battle system isn't like Bioshock or Borderlands. You've got to put some strategy into killing your enemies instead of just hitting them with some crazy elements and hiding while you heal. I'm not too good at strategy with a gun. ;D But on the plus side, the storyline is pretty interesting and it's another sandbox. There's a lot to do and you'll definitely get your money's worth in terms of play time. And all the while you play you can listen to fun old-timey music!