This is harder than I thought. The Campgrounds around Bridgeport will be closed by 10-20 except for the Crag cg which is in the middle of a sage flat.
All the FS cg are run by concessionaires with a profit motive. They may or may not be open no matter what the FS says. I would hate to pick one and then find it closed. Green springs creek may be open, but it is at the end an 11 mile dirt road. It will be in middle of your Fall Colors, It is best to check with the people running them. that will take some time.
On hwy 4 out of Markleville there is a county own campground and a BLM campground. Maybe I can cajole one of them. The BLM cg may be ok for disbursement camping even if closed, with Grover Hot Springs as a fall back.
I will be doing some riding and fishing up there, I will find something.
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