"The man is washing himself in a bathtub."
Translation:Mężczyzna myje się w wannie.
Theoretically, you can put 'się' on any side, but sometimes, one seems a lot better... "się myje" sounds a bit unnatural to me, but I believe that it's still technically correct, so added, anyway.
Actually, 'się myje' sounds to me as if your sentence was an answer to "Where does the man wash?"
After giving it more thought and checking a bit, I conclude that you are not wrong at all. Maybe it's still more often used for bath, but seems that it's perfectly okay to "kąpać się pod prysznicem" and even "brać kąpiel pod prysznicem".
Though 'kąpiel vs prysznic' will definitely be understood as 'bath in the bathtub vs taking a shower' (what is better, what is more economic, what is healthier)