Well, think about this first.
What do you want?
If you just want to end up talking to her, then talk to her, quit being such a wuss. What's the worst that can happen? She doesn't want to talk to you, and you quit your staring activity? If staring gives you the hard-on of your day, then I guess you'd suffer a big loss, but otherwise, you have ABSOLUTELY NOTHING TO LOSE.
If you want more. Date otherwise, then just do it. I'm serious about this. Talk to her, get her number, call her up, ask her on the date, go on the date.
Think about this. If you don't do it, the next jackass with the balls to do it will do it and end up going on a date with her. And you'll never know.
The worst that can happen is rejection. But rejection is your freedom. It lets you know the truth, it helps you not waste time, it gets you on with your life. If you want to know the truth, the only risk is rejection. But rejection isn't the worst thing that could happen to you. She could pull the 9 from her back pocket and shoot you up. Don't lose your chance because you were too scared to do something.
I hate the pansy sayings, but it is true. It is better to do something and fail than regret not doing it and wondering if you ever would have suceeded.
Besides, if you can't even muster up the courage to talk to her, where do you place yourself at on the manliness scale? No where where she could actually respect you. I'm sorry, eye contact doesn't get you the girl. Getting the girl gets you the girl. Get up and do what you need to do. Just by doing that puts you at a level above most guys out there. Do it for you. Not for her or anyone else.