If you were redoing the bathroom anyway, I think it would have cost less than you think for an electrician to pop in and just do it right for you. They see things that you may not, from what I'm reading, there is only a few hours at the most for what is taking a week of delayed finishing...?
If you can power the outlet with the direct hot from the switch box, great, if not then it'll be switched with the light til you decide to do it right.
Ok so tested it today and the light works when wired from the new GFCI outlet!
A couple of questions regarding the ground though. I only have a hot and neutral coming into the outlet. The new copper wire has hot, neutral, and ground wires. The outlet has a ground screw and the light fixture has a ground screw.
I wired it the first time and didn't ground anything anywhere. When I turned the circuit on the outlet tripped. I reset it and the light came on and everything seemed fine.
So my question is...should I ground the new wire going from the outlet to the light fixture to the GFCI outlet ground screw and then ground the light fixture? Obviously a wiring newbie.
Thanks for all your help!