Interesting challenge, which clearly doesn't involve a rental car - so have a browse at http://www.washfly.com

Other points include:
As mentioned already, 3-a-day to IAD v. 1 to BWI. Backup is always worth having.
Depends where in DC you're heading for: BWI would be a PITA for where we go, but for the centre of DC possibly credible.
DCA - meh. Connecting flight OK if you have hand-luggage only, and it drops you right on the Metro.

You're going in the SUMMER?