I can't speak for Rt 355 in Frederick, but as you get closer to DC, it becomes a major 4-lane, no shoulders, wall-to-wall traffic commuter artery.
Alternate from Frederick: Rt 15 to Point of Rocks MARYLAND side of Potomac River. Transition to C&O Canal Towpath. Take towpath to DC, or at White's Ferry, cross into Virginia and via Rt 15 and side streets connect to Washington & Old Dominion bike trail in Leesburg. (Rt 15 from Point of Rocks to the White's Ferry turnoff is unrideable - 2 lane fast traffic NO SHOULDERS). Caution - the C&O is packed gravel, dirt, and loose gravel in a few spots. Probably rideable on touring tires, NOT on skinnier pure road tires. Also, check various bike routes available at the bikewashington.org website and on the Potomac Pedelers Touring Club
http://www.bikepptc.org/ site. Maybe there are sections of their rides that work for you.
Check other threads for routes between Baltimore and Washington DC if that is an option. Is there any info on the East Coast Greenway site
http://www.greenway.org/ that might help? (unfortunately, it runs through southern New England, so you still have to get south somehow.)