It seems to me this should not be difficult. One assumes that, since you're applying for a position with the public library, you're reasonably literate. One also assumes you've been getting around without a car for at least a while. Simply point out, as concisely as possible, how you get around the car-less challenge in your daily life....point to alternatives, make certain to present your reasoning as to why those alternatives will not take more time or cause other problems. If your proposal is crafted well, the lack of vehicle should be outshined by your ability to express yourself.