I installed a Jensen marine radio in by bathroom for similar reasons. I wanted waterproof controls for the system, and going with a marine system instead of something designed for the home was by far the cheapest way to go.
For power, I found a high power 12V supply from Mouser Electronics for arund $60, but it's a semi-open chassis, so not sure I'd use it if I did it all over again. You could also look at using an Xbox power adapter -- you can get a 203w on eBay pretty cheap, and you'd have a nice clean brick instead of a kludge.
The wall depth issue noted in previous posts would seem to be an issue. My system has two pieces, sot the only thing on the wall in the bathroom is a surface mounted control panel, with the main unit and power in a nearby closet.