Aha! I solved the problem! I are genius!
Okay, so the fishbowl cover is in 2 parts, right. There's the glass bowl with the screw, then a plastic upper part where it screws in.
So I thought, "Hey, I wonder if I can twist the glass part and unscrew it that way?"
And it WORKED! Woo!
So I got the cover off, changed the bulb, and then tried to remove the screw now that it wasn't screwed into anything. It won't budge. It's somehow attached to the glass part, and won't budge.
I think it's time to leave the glass part OFF my light fitting.
Anyway, gotta get ready for Uni. Thanks for the help Funners.