Don't think you can go to swinging bridge anymore..didn't they make browns park a wildlife refuge? (PS..the first 8 miles is day section, but below little hole, (red canyon and swallow canyon) you can camp...I did a 2 boat late season duckie trip...lovely section...there's many camps for small group, with fire pans fresh cut stacked wood, raked tent sites, picnic tables, and a mint on your pillow in the morning! I didn't know the names of anywhere we camped...the trout will drive you nuts...so many, i snagged on with my lure in the back~!
Call the blm in vernal or usfsin dutch john. don't know if they leaves the mints in sept.