[MovedGoalPosts]

Getting an output from the STB to the TV in another room is the simple bit. As Chris T says, simpy run a standad co-axial aerial lead from the STB to the bathroom LCD TV. Picture may not be quite as good as if you had a scart lead connection, but it will suffice.

The bigger challenge is the changing channels bit. This depends on the type of STB you have. Most PACE STBs use IrDA rather than the more standard IR for remote control signalling. In which case you probably need the DigiEye remote signalling.

Indeed DigiEye also offer a remote video and signalling so you could, almost wirelessly connect the STB output and control channels too.

Of course, electrics in bathrooms are a major safety challenge, and if you are doing any wiring alterations in there to accommodate this, that is now subject not only to electrical regulations but Building Regulations Approval too, making such alterations outside of the remit of the DIYer.