VERY... Carefully - if you value your arms and hands, anyway! I used to work in a vet clinic MANY years ago (real life), and we gave cats baths - mostly to get rid of any fleas that the cat had, though sometimes after surgery (once the cat has woken up abit). Had to be extra gentle around the stitches! Other times, it was just a request by the owner. But yeah, you CAN bathe a cat, but just be ready for those sharp claws!
As far as the game goes, I don't think there is a way to bathe your cats.