Shut off the circuit breaker that protects the circuit to which you'll connect the new light. Bring the probe of the no-contact voltage tester near a wire or outlet on the circuit. If the tester lamp stays off, the power is off. Always verify the power is off before working on a circuit.
Install sheathed cable between the bathroom's electrical outlet and the wiring box for the light switch. Install a second cable from the switch wiring box to the shower's light fixture. Remove 8 inches of cable sheathing with the cable stripper from both ends of each cable.
Strip 5/8 inch of insulation from each wire end. Place the wire ends into the wire bending hole on the stripper and twist it into a 180-degree bend on the wires in the receptacle box and the switch box, but not the wires in the light fixture wiring box.
Remove the receptacle's mounting screws and pull the receptacle out of the box. Remove the tape that covers the two "Load" terminals if it's a GFCI receptacle. Loosen the terminal screws. Place the bare ground wire on the green terminal, the white wire on the silver terminal, and the black wire on the brass terminal. The bent wire ends wrap clockwise around the terminal. Tighten the receptacle terminals firmly.
Twist the two bare ground wires tightly together about 5 inches from the ends. Wrap the end of one ground wire around the green switch terminal. Place the black wire from the receptacle on one switch terminal, and the black wire from the light fixture on the other terminal. Tighten the switch terminals firmly.
Hold the green fixture wire together with the bare ground wire in the fixture wiring box. Put a wire nut over the wire ends and twist the nut clockwise to tighten it. Repeat for the two black wires and the two white wires.
Install the cover on the fixture's wiring box. Place the switch in the switch wiring box and install the mounting screws. Mount the receptacle to its wiring box with the two screws removed earlier. Install cover plates over the switch and the receptacle.