How to approach a (shy?) girl that stares at me?

[Michael]

There's this girl that's kinda cute (who goes to college with me). She's not very attached to any of her friends (male or female), and sometimes she seems to be just in her own world.
However, I've caught her staring at me several times, and since she usually acts like I've said before, it was kind of shocking. And it is this penetrant, wide-open eye stare, which lasts for a couple of seconds (even though sometimes she does look away quiclky).
We've only talked once (it was pretty short and there was smiling). After that I joined my group of friends and she was with hers. After a while, I randomly looked up and there she was staring at me with that beautifuly penetrating look again, completely absent from her friends' conversation.
But apart from that one time, all there was was just the staring (always from some safe distance, might I add).
What should I do?
Thank you!

PS We're not friends on Facebook and we don't have each other numbers.