It's easy to head toward Skyline Drive from DC--just take the W&OD trail westward. It's a nice, paved, rail-trail. You'll need to first take the Custis Trail in Arlington, VA, for a few miles to connect to the W&OD. The two trails will take you 2/3 of the way to the north end of the national park.

I don't think it would make sense to bike thru Baltimore. Either go around the west (longer but hillier and prettier), or the flat (and boring, IMHO) Eastern Shore after the Cape May-Lewes ferry. I believe there no longer is an official shuttle across the Bay Bridge, i.e. you need to find somebody who will take you across the bridge, but I'm not 100% sure. If you decide to go west of Baltimore, you could go west from Philly thru Amish country east of Lancaster, PA, very pretty country.