I wouldnt even try it. I have two machines, one is a single-core, socket 754 with a Radeon X800 Pro. No way I would bother with Bioshock on that.
My other system is a 4800+ Dual Toledo core (939) with a GeForce 7900GTX. That plays alright.
Nobody who spends money on a good video card is going to settle for a single core CPU these days. Duals are very common and priced well, and quads are becoming more common every month.
Same with RAM. People were pissing and moaning about the heavy memory requirments for modern games and OS's, until they finally realized that the stuff is dirt cheap nowadays.
For example:
http://www.newegg.com/Product/...x?Item=N82E16820220145
If you wanna play hi-end games, spend a little extra on RAM and a dual-core CPU, you'll be glad you did.