Can I run a receptacle from a GFCI in the bathroom to another room?
The bathroom needs its own circuit, the only current code compliant way to go to another room if it is also a bathroom. Added per @harpers comment. If the bathroom loads include the fan and light then another bathroom can not be powered from this circuit. I like bathroom lighting to be separate because if the wife or girls plug in a curling iron and use a hair dryer at the same time it may trip the circuit and put them in the dark.