Day and Day
The main reason I started looking at this thread was to try and get an answer for the question that has been troubling me. Now I feel like I'm a step closer by looking at this and getting some rough ideas of how to address this situation.
I have done this before, and the best place I found to start is with chatting about the class. Talk about an assignment, a lecture, or anything. Get on a good to know basis with her. Then, after a class or two, you can shift the conversation to topics outside of it. If she seems unresponsive, I have discovered that saying "Wow, you sure seem energetic today" usually gets a laugh out of her.
Try this out, and then when there is a test coming up, Number Close on her by asking if she wants to study together for it. Do this, and then report back here with results.
"There is no better than adversity. Every defeat, every heartbreak, every loss, contains its own seed, its own lesson on how to improve your performance the next time." - Malcolm X