There's no reason why you can't ask her out. Of course having your own car is ideal, but it's not a requirement by any stretch of the imagination. When you mention not having a car, don't be like "umm, wellllll you see." Just tell her and be done with it. Be confident and go on a date if you like her. The only two outcomes of any situation are that it works out or doesn't. You work together, she's already likely noticed that you're not driving to and from work. Especially in a city with public transportation, it's not that weird for someone not to drive. It should be the same the other way around also.
I've dated females that didn't have a car and didn't have any problems picking them up and such, because I liked to hang out with them.
It can be difficult if it bothers you to have a girl drive you around (sometimes it can be hard to get over "The man should drive" mentality). That being said, I dated with no problems back when I had no car. If she requires a car, she's not worth your time.