Consider your options.

One is as neilfein suggested, heading into Philadelphia. From there follow the East Coast Greenway to DC.

Another is to head due south, to Cape May, cross on the ferry, head west across Delmarva to the Annapolis bridge, and get a shuttle over it. The Bike Washington website has detailed instructions on riding from Annapolis to DC - or to Greenbelt, where you can take the Metro into DC.