quoted text -
I don't believe it is code compliant to switch the neutral, although my NEC is packed away in a very safe place.
As I said in my previous post however I'm certain that a receptacle in a bathroom by current code either needs to be on a 20A circuit that serves only that bathroom, or a 20A circuit that only feeds bathroom receptacles (that is, you can feed receps in more than one bathroom - not sure how many - but only if the circuit feeds *only* receptacles, e.g. lights, fan, etc. are on a different circuit.)
If the OP's bathroom does not have a recep then I am guessing that it does not have a dedicated 20A circuit either and likely the light and fan are on a 15A circuit that is a general lighting/recep circuit for that area of the house.
nate