Don't misunderstand me - Your question is a VERY basic one. So my first 'reaction' is if you don't know what you're doing, ESPECIALLY when it comes to electricty (which you CAN'T see), you may be in a position to 'hurt' yourself. At the same time, I respect your desire to save some $$$ and do this yourself.
With the latter thought in my mind, spend some of the $$$ you'd otherwise spend for an Electricial to do the job and go and buy yourself a GOOD, introductory book on Electrical Wiring. The Home Centers have them as does Time/Life and Reader's Digest. Even a Bookstore in the Mall has them. You will find MORE useful info in there that will educate you more than we can do from here.
For example, you may need to run a separate, new 3-wire line to the bathroom. You WILL want to install a GFCI outlet in the bathroom too. Even more, maybe the outlet box is currently installed in an UNSAFE location, like right next to the bathtub, or something.
There's more to just running wires and hooking them up ESPECIALLY when it comes to electricity. Do yourself a favor - Educate yourself on basic electricity, then more on up to electricity 'around' water. Sorry, but it's the best advice I can give you (and anyone else thinking the same thing with your particular 'background'.)
Be safe. My best to ya and hope this helps.
Jay J -Moderator
PS: Christmas is coming - Find the book and have someone buy it for you ...
PPS: God Bless America!