It's better to try and fail than to not try at all. Beyond that it's through doing this that attempts after it become easier. Is it hard to put yourself out there? Sure. Do you run the risk of being turned down? Yep. But in doing we become stronger and more experienced.
This world is full of people. Take a risk, you don't know her so do the simple and awkward thing. Introduce yourself, "Hi, I'm so and so. I have noticed you looking my way more than once would you care to talk?"
You already have the que of her meeting your eyes or looking at you more than once. So either you are visually appealing to her or you are a oddity to her. Either way put your best foot forward and make the attempt. The out come may just surprise you.