There's nothing in DC that I know of, and most of the stores I knew of in the close in suburbs have closed. There is a G Street fabrics in 7 corners. It's on the SE corner of Arlington Blvd (US 50) and Leesburg Pike (VA Rt 7). There should be buses going out there, but a car would be helpful. They have lots of different kinds of fabrics, including exotic fabrics, although their quilting fabric shelves have been pretty bare the list few times I've been there. The web site gives directions to take Metro to another location.
http://www.gstreetfabrics.com/
Seven Corners Center
6250 Seven Corners Center
Falls Church, Virginia 22044
Phone: 703-241-1700
You might want to go to the textile museum. I don't know that there's anything to buy there, though.