Why make it sound like it's just for studying purposes? You're creating a friend frame by doing that. Just say exactly what you want and establish yourself as a flirty, potential hookup guy.

When you say it is easy to talk to her, how do your conversations go? Does she keep her attention on her book and politely answer your questions and then go right back to reading? Or does she stop what she is doing, close her book, and have an interactive conversation with you?

Even better than asking her for her number though would be to try to get her on an insta-date right there on the spot. If you are already talking to her, then it shouldn't be much problem. While you're talking you can just say something like "I'm about to head to the cafe for some coffee, you should join me." or "I've got a great idea! Let's take a break from these books and go grab some coffee."