Use the distance between you to to your advantage: Talk with her. About anything and everything. This is a great way to get to know each other without any of the up close issues. If you really think she might be a keeper and want to surprise her, write her letters. A forgotten art.
Shortly after I met my wife, I went away to school in another state for several months. We wrote letters nearly every day and talked on the phone twice a week for hours. (she had access to a watts line). By the time I came back home, we knew a lot about each other. And we learned it all without having to worry about where we went on dates, or who liked what food, or any hormone driven baggage.