Well I'm a high budget computer builder so low budget computers aren't my 100% specialties, but I guess I'll ring in my 2cents.
I say just keep your current configuration and just save up all your money for a new pc. I say that because I don't know your PSU(power supply) so a new GPU(gfx card) could overpower the PSU, so then you'd have to buy a PSU, theres 2 purchases already.
Then if you did buy those 2, then you could get away with 1gb of ram, but playing Bioshock or any newer game is really gonna tax your ram loosing quiet a bit of performance. Then also your CPU is gonna start bottlenecking your GPU.
I've built 3 Quad-core DX10 computers in the last 2 months that were on a budget, and they were only ranging from $1300-1600.
and those have had thing you might not need, like DVD drives and HDD's(hard drives). So my recommendation would be to save up your cash, and $1,000 will get you a Quad core DX10 PC fully ready to play any game out on high GFX and future games as well (cough....Crysis...cough)
P.S. you can run the Bioshock Demo on SM2, but its has Extremely long loadtimes and textures are little weird, and this is all with couple file tweaks.......but it's really not worth the time, but it is possible.
And make your friends jealous, even with simple benchmarks