A representative from Bridger-Teton National Forest sent us an email to answer your question - here's what they said "Since July of this year all our dispersed camping sites have been equally full and expect the same to continue into the end of summer in our area." Public Affairs for Bridger-Teton National Forest

Not that I have seen. They are much much smaller than the first few camp ground areas if you will. Last time I was there it myself and 2 other groups and still plenty of room if you’re friendly. Also if you don’t mind a mini hike there are some even better solo spots you can park at the bottom of and hike up a hill and set up a camp.

These sites take a bit more 'work' to get to - but with a small rig and a bit of bravery - you may have them to yourself. Most people stop at one of the group areas below. If you can get up to site 27 and it's free - it's the most epic of the epic.