I want to ask out a girl that stares at me a lot, but I don't even know her? Please read details?

There's a girl in my class that sits all the way across the class from me and we sit in rows that are farly spaced. I never talk to her but i catch ehr staring at me a lot, and when I do she doesn't even look away..she just keeps staring. I want to talk to her but I don't sit anywhere near her. Should I just make the effort to get to know her or should I ask her out for a movie? THANKS FOR THE HELP, MEANS A LOT!