My muscovi drake is a little stinker too. I have a kiddie pool and a bathtub in the run and there's a pond and streams he can access but nope! The only way he will stay in the bath is if there is a female to mate with, and I'm pretty sure my girl doesn't bathe as often because of that (but she really enjoys a soak in my bathtub indoors, all by herself! and now that she has a tub outside, the drake doesn't notice when she's in there as much as the kiddie pool.)
I had asked my friends who I got my eggs from when i first noticed it and they too said their drake was dirty and didn't like to bathe but their females were clean.