I would say you have been talking to her a while and you should just see how it goes when you are next together. The fact that you like her and she seems to want you to have her details, home number and all shows she must like you. I can't tell you the hows or the when because that is something which you have to choose for yourself, seeing as how it is you who wants to take the chance and see what happens for the two of you.
However I would want to get to know her well enough to feel comfortable with the fact of asking her out. It's not difficult to do it's just something you need to know how to approach. One thing I would say is if you find it difficult to talk then best thing to do would be have an idea of how/where you should ask her. Also be prepared for rejection because you never know she might prefer to have just a friendship with you for the moment.
Good luck I'm sure you will be fine! Feel free to PM if you feel it's needed.
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