RSB,

Some of the walls of your bathroom with have another room
on the other side. Do you have any "always on" outlets on the
opposite side of those walls? If so, then it should be easy to
install an outlet in the bathroom opposite the outlet in the next
room.

There are many other solutions, but I'd really rather not get
into them. I feel that you may need both a book on introductory
home wire plus a mentor. I'm not trying to be nasty; just
realistic. If you want to do your own wiring, then you really
need to spend some time learning the basics.

Gideon