Most of the women I've met in the last few years seem impressed when I say I prefer cycling to driving. That part of my lifestyle doesn't seem to be a barrier.
In more practical terms, car-free dating is not easy for me. I'm quite visible and well known here so if I want any privacy on a date, I need to get out of town. (At times, I've been interrupted when I'm out with friends in town.) Because of some of the logistics involved, a car is now involved.