electric in bathroom
I would investigate a bad contact in the fixture first.  

Tighten/loosen the bulb slightly. Try gently wiggling the bulb.  If the light comes on, it's probably a bad contact.

If the light does not come on. Remove the bulb, and with a flashlight carefully look into the empty socket.  You're looking for corrosion, discoloration, a bent, misaligned, or damaged contact. If you see any damage, replace the fixture.

If everything with the socket looks good, you'll want to look for loose connections.  Turn off the power, and inspect the fixture wiring.  If you don't see any problems, check the switch wiring.

If everything still looks good. Use a multimeter to test continuity through the switch.  

If you still haven't found the problem, it might be time to contact an Electrician.