A GFI (Ground Fault Interrupter) circuit or receptacle must protect an electric fireplace in a bathroom. Fireplaces are not watertight, and you must protect them from water ingress. For this reason, you must install electric fireplaces away from tubs and showers. For this reason, we do not recommend wall mounting a fireplace in a bathroom.
The best way to solve this is to recess it into a wall. Ensure the ceiling exhaust fan is operating when bathing or showering to help remove excess moisture from the room.
It's always a good idea to inquire with local building code officials about any requirements that might need to be followed in your area.