...you can indeed bathe cats. With great difficulty. Using a method that involves two fully clothed humans standing in a shower stall, in order to wash one small kitten. Some clawing took place, although thankfully, not too much. And the end result is one absolutely miserable cat.
But she smells really nice. And her fur is soft and smooth and sleek; not dusty or dirty at all from her various explorations behind our appliances. So in the end, it was worth it.
(Yes, those are my feet in the picture, and I am wearing ancient pajama pants.)