Actually, you are going to have a difficult time getting to any quilt shop without a car. Jinny Beyer's Studio (in Great Falls) and the Virginia G Street shop (in Centerville) are both too far from the a metro stop without taking a cab. I think the price of retail space near the district is too expensive for a quilt shop to survive.
For a current list of shops that are nearest DC, here's a list of the stores participating in the annual shop hop:
http://www.quiltersquest.org/shops.html