I have the pow-ah!

A silly/dumb question: if a lightbulb in a fixture is burned out, but the lightswitch is on, is power actually being used? That is to say, is my energy bill going up (albeit by only a teensy bit) because I have an outside light that needs replacing, but the switch is one of those weird ones where either position could be "on" and so I don't know if it's on or not?