You can only accomplish this if there is a white neutral wire at the switch. If the original circuit went to the light first, then there is only a loop to the switch which interrupts the black hot wire. The cable from the light to the switch may have black and white, but the white should be taped or painted black where it attaches to the switch. In that case, you will have to fish a new cable to the proposed outlet.

house, you cant bring one in from the basement or attic?

Depends on what else is on that circuit. If the bathroom receptacles are on the same circuit as the light you can not tap that circuit.
If the swich has a white and black wires connected to it you don't have a neutral in the box and can not tap a receptacle of it.

Thanks for the feedback. I'll have to check what's connected. Good thing I didn't make a whole in the drywall!

It's a finished home and I'm not sure if I want to go fishing. The attic is a possibility for sure though.