Cherry Hill is a clean, commercial and expensive (around $60.00 per night) campground (Campground Reviews
) that has a bus stop that gets you to the Metro, which gets you just about anywhere.
Greenbelt Park is run by the National Park service - inexpensive ($16 or $8 with senior card), but dry camping
(with restrooms without showers) that is about 12 miles from DC, and a 4.5 mile drive to the Greenbelt Metro station. One note - there is a posting on the Greenbelt web page
warning about ticks, and a couple of complaints about the same at Campground Reviews