Just two dads biking around the loop with four of our kids in trailers. In real time, it took us about 30 minutes. Go fast enough and the skeeters won't catch you!
The Virginia side of Assateague National Seashore (Chincoteague National Wildlife Refuge) has a nice, easy paved trail called the Wildlife Loop.
Although you have to pay to drive to the beach, you can bike onto Assateague for free (including all the way to the beach, on a trail that shoots off from the Wildlife Loop).