My roommate is a little....uh...eccentric?

Try to find some common ground, if you think she's weird then you can ume she knows she's weird. Maybe she doesn't expect you guys to have anything in common, so maybe mention how you like one of the songs she listens to, or ask her stuff about her banjo. This will spark conversation and I think it will work:) sometimes you just have to pull people out of their shell, its not easy but they always turn out to be the most interesting people you'll ever meet. good luck!