How to let a girl on Facebook know I'm interested in her?

[ZLD]

I recently became Facebook friends with a girl whom I knew like an acquaintance through a college class we had together. The semester is now over, but starting a couple of weeks before that, I've thought about asking her out or something.

Facebook messages/chat is currently the only way I can contact her, but with her apparently being busy quite often, she and I haven't had an actual chat yet. When we get a chance to talk through FB (or maybe some other means like text messages), how can I let her know that I'm interested in her without coming on too strong? Since we should probably get to know each other a bit as friends first, what could possibly direct the conversation toward that topic?

Our first online conversation may be several days away, or maybe it'll happen within a few hours of this question being submitted. Who knows. *shrug*
After we became FB friends, I sent a few messages about getting to know each other as more than former classmates and having a conversation sometime. But I don't know if I should send any more before she replies from her side of the chat window. I can see how online messaging on a semi-daily basis could become annoying, and of course, this could just be a matter of impatience on my part.