It would have to be on all the time ...all it would do is pull air out of both rooms while it was switched on .. when it was off ... the smell would go thru to your bathroom .
Bathroom extractors and fans are not realy much good for what you want .... what you could do is cut the ducting in your room ... add an excraction fan and filter in your room and suck the air out .... and use the bathroom ducting as the INTAKE ? .