How many bots can I expect to run on a setup like this?

[Nostran]

AMD FX-8350, Gigabyte GeForce GTX 285 - System Build - PCPartPicker

That's what I'm looking at now. The case will be purchased later.

What will be the limiting factor in this build? And how many bots can I comfortably run?

 

[arielmz]

Somewhere at 8-10 bots... the limit factor is the heat on the proc so far... with a decent water(xspc) (theres a nice kit for 150u$) u can get somewhere to 12-16 bots.

(This kit can be expanded for vga/ram etc with a bit extra $$)
XSPC RayStorm 750 RS240 WaterCooling Kit [XS-750-RS240] from XSPC Online Store

or the classic h100i (about 30-40% worst on reviews about same price)
Newegg.com - CORSAIR Hydro Series H100i Water Cooler