A couple of my friends camped last year. They stayed at the first, but biked past the 2nd to check it out:

1. Stay close by in a trailer park. The best candidate right now is Madison Bay Campground, 9.4mi 14 min from Blackwater.
4814 Canning House Road Madison, MD 21648 410-228-4111. their description says: Enjoy spacious campsites, boatslips, showers, laundry area, restaurant, and a game room. Call for more information. They do not have a website. I called but got a private voicemail (Candy Hughes).

There are a couple other trailer parks. Taylors Island 14.4mi 22min from Blackwater.
Here is the only review I could find (from a kayaker): Review of Taylors Island campground:
Camping in Dorchester County is limited to three private campgrounds that mostly function as trailer parks, and two of them are on Taylor's Island. Given its tiny marina--a mere notch on the coastline--the Taylor's Island Family Campground ([410] 397-3275) is most convenient for a trip to nearby James Island, and it's but a short drive to the put-in for paddling to Barren Island. Its small area for tent camping is in the marshy pine woods behind the last row of trailers, a short walk to the showers, a convenient store with a liquor license, a pool room, and a shack filled with video-poker machines. The most prevalent patrons here are beer-drinking men in baseball caps telling fish tales by fire pits, their boats nearby, hitched to pickup trucks. But paddlers are more than welcome to join in the fun.