The Claytor Jungle Hammock is built so that you can use as a bivy if needed,
see this page. On the one hand you get (if properly ordered) a double bottomed hammock so that it is easy to slip in a pad between them, on the other hand this rig runs a bit on the heavy side. You can lighten the load a bit by going with a silnylon tarp (purchased separately from someone else).
It is possible to rig an HH to be used as a bivy on the ground. Should have a ground sheet, and a movie camera to record you getting into and out of its bottom loading style.
But you can find suitable trees. You can do like neo did, and hang your hammock across the trail between a couple of trees. You might want to check for moose droppings in the area first though...