You're right... it could be very difficult to find things to talk about with someone who doesn't tell you nothing about herself... but just think that she may be shy.. and most probably she still doesn't have full confidence in you.
So i suggest (that's of course if you really want to get to know her) that you start telling her about yourself.. things you like and things you don't.. try telling her about your hobbies.. where you like to hang out and what you like to do.. she'll get to talk.. at least she'll comment about the things you're telling her and this way you'll start, bit by bit, to know more about her and form some image of what she might be.. then you could tell her what you think of her and what you got to know.. and if she's interested then she'll sure want to tell you whether you're right or wrong in what you think of her..
And i'm not telling you that this is easy.. but then - again - it all depends on whether you really want to know her or she's just like any chat friend and you might as well talk to anyone else...