As far as I know, Cherry Hill RV Park is the closest to DC
Cherry Hill Park is the Closest Campground to Washington, DC :|: Cherry Hill Park. Check where the event is and see is there a Metro station near it.
If you are able to get a site at Cherry Hill, there is a Metro bus stop right outside the park entrance that goes to the Metro Rail station. Here is a piece of advice from someone who lived in the DC area for about 8 years. If you can get where you have to go on the Metro, DO NOT DRIVE anywhere in the DC area.
Traffic is horrendous. Parking is impossible. If you don't have a TOAD, and you absolutely need a car,rent a car while in the DC area. Parking an RV in the metropolitan area would be beyond impossible. You might check Enterprise near where you might camp. They probably would deliver to the park.
But again, if you do not need to drive -- take the Metro -- you'll thank me later.