Invite her out to coffee. Dating is all about finding out about a person, be it before or after you become fully committed.
Just don't go for a movie. Go for a coffee, and preferably have one or two topics to get you both talking. Dates are so much easier when you have something mutual to talk about.
Last "date" I went on (wasn't really one, but was similar), it involved the guy going "I'm bored, and I heard that there's this new bar around. Wanna try find it?". Which resulted in us talking about bars, trying to find places, stopping at a few pubs. It was good fun, had an awesome time chatting and led to more interesting things later on in the month. *eyebrow wiggle*