to the forum, O Prince of Darkness
There are plenty of techy people around here, hopefully one of them will have some ideas for you.
Personally I'd have thought it was as simple as connecting the TV in your bathroom to the STB via a length of coaxial cable, splitting the output from the STB if you're already using coax to connect to your main TV. But I don't know the details of how/whether that works, so I'll leave it to others to advise you.