OK.
First, just about anything is possible.
LMGTFY:
Obviously the acoustics is a big thing. Considering the humidity in a bathroom, and the tendency toward reflective surfaces, treatments are tricky though possibly achievable in terms of deadening the walls and what not. I suspect with a little research you could find ways to do panels that could be added to dampen the reflections a bit more and be resistant to mold and mildew. Beyond that, weatherproof speakers.
All of this could be achievable, sure.
If you are in business for yourself, I'd suggest looking for an acoustics person you could consult with. His/her time would cost you, but be deductible in the end, even if the project goes nowhere.
There seems to be good products on the market as demonstrated above.
Please send me your address so I can bill you for my consulting fee.