That's terrific! Don't think it didn't occur to her that you might be asking her to get to know her better. That she accepted doesn't necessarily mean that she is interested in you, but it means she probably doesn't dislike you. It's a good place to start.
I suggest the first few study sessions you just stick to studying, and not worry about asking her out. This is the perfect opportunity to get to know her better and feel more comfortable in her presense. If you two get along then you will see that it will become easier to ask her out.