Slight factual correction for Maryland, straight from the state code.
§ 21-1205.1. Bicycles, motor scooters, and EPAMDs prohibited on certain roadways and highways; speed limit.
(a) In general.- Notwithstanding any other provision of this title, a person may not ride a bicycle or a motor scooter:
(1) On any roadway where the posted maximum speed limit is more than 50 miles an hour; or
(2) On any expressway, except on an adjacent bicycle path or way approved by the State Highway Administration, or on any other controlled access highway signed in accordance with § 21-313 of this title.
(b) Roadway with bike lane or shoulder paved to smooth surface.-
(1) Where there is a bike lane paved to a smooth surface or a shoulder paved to a smooth surface, a person operating a bicycle or a motor scooter shall use the bike lane or shoulder and may not ride on the roadway, except in the following situations:
(i) When overtaking and passing another bicycle, motor scooter, pedestrian, or other vehicle within the bike lane or shoulder if the overtaking and passing cannot be done safely within the bike lane or shoulder;
(ii) When preparing for a left turn at an intersection or into an alley, private road, or driveway;
(iii) When reasonably necessary to leave the bike lane or shoulder to avoid debris or other hazardous condition; or
(iv) When reasonably necessary to leave the bike lane or shoulder because the bike lane or shoulder is overlaid with a right turn lane, merge lane, or other marking that breaks the continuity of the bike lane or shoulder.
http://198.187.128.12/maryland/lpext...s-main.htm&2.0 if you want to see the rest of the bike regs for Maryland.
DC allows riding on roads under all circumstances.
Virgina leaves it up to the local jurisdictions to decide if riding on a bike path is required.