Some cats allow you to bathe them. I used to have two cats, one was a Siamese and the other was a Ragdoll, the Siamese was great at bath time, he would sit there long enough to get cleaned, but there was no taking my time at it or he would simply leave when he felt like he was done, but if I just got down to business and washed and rinsed him, I could get him through an entire bath, but he wanted to air dry, there was no using the blow dryer on him.
My ragdoll was different, he hated a bath, I had to wrap his feet in a towel to lessen the bloodletting, but he would sit pretty as you please for the blow dryer when we were done with the bathing part.
Cats are funny, and each has their own personality. I do bathe my (current) cat regularly, the one I have now doesn't appreciate the joys of cleanliness, but I can generally get through it without getting scratched up too terribly bad. Probably more to do with practice at this point. Lol..