Since I shower in my RV bathroom, I would install it in the bathroom, set to exhaust, to remove the humidity generated by the shower.
Another plus would be that I could open a couple of bedroom windows and turn the fan on to get air flow through the bedroom, and having the fan in the bathroom would help to minimize the noise.
So, I vote for the bathroom.
I removed the three speed non-reversible Fantastic fan from our kitchen/dinette and installed it in the bathroom, then installed a three speed reversible one in the kitchen/dinette. They are wonderful!
