I slept in Byron's trailer. It's not exactly camping, but it's closer to camping than it is to a motel. No water but it does have electrical outlets and a couple of beds, and it keeps most of the plentiful mosquitoes out. The only bathrooms available are at the bar across the street (The Split Rock Cafe), but I think it's open early and late, so there's only the 2:00 a.m. until 6:00 a.m. window that you don't have a bathroom.
There used to be a church that let you sleep in their basement, but I heard that it's no longer available, and you needed to bring your own sleeping bag.
I've also camped in the Lion's Club pavilion. Pretty dismal.
I believe that the 92-mile stretch of the TransAm from Lander to Lamont is the longest segment of the route without a motel, and if you don't count the teepees in Lamont, then the stretch is 125 miles from Lander to Rawlins.