I say, if you are unsure about a girl and her feelings, I always suggest asking her out to lunch. Nothing pricey, something like, Applebees, Chilis, TGIFridays, Fuddruckers or something like it. A sit down place that is casual. Doing this lets her know that you are interested in her enough that you would like to spend time with her exclusivly, but understand that you do not want to pressure her, like a dinner date might. If nothing else you may get good lunch company. But after one or two lunch dates, you get the "getting to know you" crap out of the way that usually makes an acutaly dinner date akward. If you ask for a dinner date afterwards and she accepts, you're in. If you ask and she declines, it may be because of a lot of reasons, I would offer another lunch date (a day or two later) if she accepts that, she may just need more time to get to know you.
The secret to courting a woman, is the lunch date. Because it is an informal date, usually spur of the moment (like the day of or the day before). There is less pressure and because she can always go back to work or school afterwards and annalyize the date with a girlfriend. (And yes, we do do that.) Good luck.