Yeah, you're pretty hosed.
I work in DC & live near Mount Vernon. You can take the George Washington Parkway to Mount Vernon without much difficulty. I go over the Arlington Memorial Bridge to get from downtown to GWP.
From Mount Vernon, you can easily get to US-1, about miles on a non-busy residential road (wave at me when you go by). US-1 can be evil traffic-wise, but even with traffic lights, you can often get places faster than on I-95 at rush hour I'm not familiar with Va Beach, but I would guess you can get pretty close to there on US-1.