| Sounds like the cover is cut real close. On my older basses, (my bc rich in particular) it tends to stick as well, but I get a tooth pick and kind of pry it out. I wouldn't do that to a really nice bass though.
What you could do, is get that toothpick, and put it in one of the screw holes only deep enough to get under the lip of the plastic, and pry it up that way. Find the spots that bind, and gently trim them. | 
