There's eye contact going on. Yet, neither I nor her have yet to break the silence. Any advice?

There's a girl who sits next to me in music, and for the last few weeks, I've been noticing the exchanges of eye contact for a short moment. So there's the obvious thing out of all this.

There's usually nothing said between both of us except for questions that 'need' to be answered. There's a big lack of the casual, easy-going conversations.

I decided recently that I should really do something about this, but whenever I get my chance to speak up, I'm stuck speechless.

Even today, she was standing with her friends on the sidewalk where I pass everyday to get home. There was that eye contact, smile. Like stagefright, I had no reaction and I feel like a total idiot walking by like that.

Does anyone have any idea how I should break the silence? or even put up a play involving my friends. I'm not afraid to pull my usual band of friends into this, as they've already discussed and solved someone else's similar situation to this.