Tomorrow, DC will close several streets around the Mall to car traffic, but you can bring your bike in and enjoy DC's unofficial ciclovia.
I really think they should make this an official ciclovia with events and programming. They close two major streets along the mall and all the cross streets for almost the entire day - something that seems to be impossible to do for even a few hours on a smaller section of road. Why not make this "Feet in the Street" and do the kinds of things New York does during Summer Streets? The hard part is already done. Sure, there will be security concerns to be dealt with, but I don't think it would be undoable.
Also re-read my still relevant post on why Metro should stop banning bikes on the 4th of July.