From Cape Henlopen, you can ride across the Delmarva peninsula to the Bay Bridge - which does NOT allow bicycle and does not provide a shuttle. (I have been kvetching to Maryland DOT for some time.) They do list a shuttle number that charges $35 per person - while the toll for two people in a car is $2.50. (I want to get arrested for trying to bike on the bridge - then sue to hold up their federal funding under TEA-21.) The best way to get across is to stop at the pullout just before the bridge and hitch. Then head into DC on the Annapolis to DC route.
From DC you can take either the C&O Canal Trail from Georgetown or the Washington & Old Dominion bike trail from Alexandria. The C&O Trail is fabulous - unbelievably parklike in the middle of a metro area. Plus there is free hiker/biker camping right on the river. It is, however, hard-packed dirt - that should be pretty hard by late June.