Traveling with several people in one car to get to one destination versus every single individual person driving consumes a lot less gas and is more economical. The Eastside is generally pretty unfriendly to the vehicle-less, and there's a lot of great stuff to do around the greater Seattle region that isn't really feasible to travel to using our horrid public transportation system. I personally don't date people who don't have a car, but it's because it tells me that their lifestyle and mine won't mesh, not for any status reason. One of the ways is to ask your date about the most interesting transportation she wants to ride.
It's not that it matters if you have a car, but it does matter if all your plans have to be in your immediate neighborhood, or on your bus line. Someone who couldn't drive their own ass around would really strike me as odd or like they were missing a part of being an adult. It's refreshing to be in a courting situation again, and also makes it easier to not fall so quickly.