How do I get the fluorescent bulb out of this fixture?
I've seen some units where the bulb wasn't designed to be replaced. Based on your photo, that may be the case here. Units with replaceable fluorescent bulbs have a "twist-in" connector on either end that's visible after you remove the cover. You may need to buy a new unit and replace the fixture. I would buy a double bulb unit, since those are almost always replaceable.