I recently moved into a new apartment, built around 1960. There was no outlet in the bathroom or within 10 feet, just a light switch. So I purchased a CFCI/Switch combo at Lowes. There were only two wires in the box when I opened it up, a black and a white(no ground wire). I wired it according to the instructions, and everything is working fine, except. The outlet will not work with the switch in the on position and vice versa, outlet works fine with the light switch off. Is this normal? I am having trouble shaving in the dark, any advice would be appreciated.
It sounds like your electrical box for the switch does not have the power source (line), only a 2-wire cable to handle the switching for the light; the line comes in at the fixture.
Unfortunately you cannot add an outlet to this configuration as-is. You will need to bring a third wire down into the box from the fixture that will act as a dedicated neutral so that you can have the outlet always powered, and then optionally power the light via the switch.
Based on what you've described, my recommendation would be to bring in an electrician to handle this task for you as it requires pulling a new cable from another junction box and correctly wiring it up.