My time has passed (56, married, two kids) but here is an idea I wish I had thought of when I was carless (age 23-28). It depends on where you work, where you live, how far you travel to work, how much you earn, etc., but there is a good chance that if you have no car you have some surplus income. So here is the idea.
Go out and look at a small new car, find out how much it costs. Call the bank, ask them what the monthly payment would be for a car loan on that amount. Call the insurance company and ask them what the insurance payment would be, and divide it into a monthly amount. Use the mileage figure on the car's sticker, and your round-trip miles to work, and the current price of gasoline, and calculate how much it would cost in just gasoline to drive for a day, then multiply to a monthly amount. Find out how many units of 3,000 miles you would drive to work in a year, multiply by $25.00 (for an oil change), and divide that into a monthly amount. Find out how many units of 7,500 miles you would drive in a year, call the car dealer and ask for a ball-park price of a regular 7,500 mile check-up (minus oil change since we have accounted for that), mulitiply that price (it will be very approximate, but is must be considered) by the number of maintenance visits a year, and calculate to a monthly amount. Then add up all those monthly amounts. That is a pretty firm figure on how much it would cost you each month to have a car.
Then, open a dedicated savings account and start putting that amount into it religiously every month. To be fair, use that account for bus fare, bike maintenance, and any other transportation expenses, but NOTHING ELSE.
The final bit of setup, find a car-rental place nearby and rent a car once a month for a day or a weekend. Use your transportation account; you'll still come out ahead. Get to know them, get to know the procedures, so that when you want to rent a car the wheels are greased, so to speak, and you can get one on short notice and without any trouble.
So now here is the execution. When you have a dating opportunity, put off any spur-of-the-moment activity (no reason necessary if the person doesn't know you well) and when it is time for the outing, rent a car. Arrive in the car, just like a normal person. Say nothing about the carless concept. Your mission here is to show nothing out of the ordinary and let this person meet you without being mentally sidetracked by the carfree philosophy.
If a second date opportunity materializes, rent a car again. Show up in it. Say nothing about it. Proceed in this way as long as you want to (you still should be coming out ahead, financially). At some point, she will wonder why you show up in a different new car every time.
Now take the opportunity to explain. But depending on the person, your explanation may vary. You could bring up the carfree philosophy (oil wars, pollution) but even if that is your main reason there are others. You could say that you are saving each month money to purchase a car because if you pay cash you won't have to pay interest and that makes good financial sense. You could say you are saving money to buy a house first because it will increase in value whereas a car does not. You could say you want to take a trip to Europe before you take on a car payment (and would she like to go along). You could say you are trying to build up an IRA now so you can let it sit for the longest possible time and then retire early. The point here is to get across the idea that you are not some sort of bum just because you don't own a personal motorized transportation appliance, but that there are other things that could be done with that money. Depending on how much money is in your account at the time, you could explain that you could go out tomorrow and write a check and drive away in a car, but what would that prove.
Now, once the person knows you a bit, you get to make the decision, instead of she summarily dismissing you because you don't have a car. If you have had a chance to demonstrate that you are normal (i.e. car-driving), but that for some reason (whatever your reasons are) you do not own your own MTA (motorized transportation appliance), and she can't get her mind around that concept, then, sadly, she might not be a keeper. Although, one would think, anyone who has mastered basic arithmetic should see the logic of your situation (says one who just today spent a thousand dollars on repairs to two cars).