Catamount is an excellent takeout and a good day float from State Bridge. You're not likely to encounter anyone else along the way. However the five river miles below Catamount are really pretty, there's no road through there so except for when a train passes it feels very remote. There's a great campsite river right just past some power lines about a mile or two from Catamount.
Once you emerge from that canyon there's a takeout just before Burns next to a RR abutment. Its steep and is a better put-in than takeout but its doable. A mile below that is Rodeo Rapid, AKA Landslide Rapid. Run this river right,(which isn't all that easy to do because there are two big waves just above the bottom hole which has a nasty pointy rock in it).
Below Rodeo/Landslide is private property, but the Glenda the manager there will let you use that for access for 5 - to ten bucks or a 12 pack of Bud Light, if you are a non-commercial float.
The next 8 miles are mostly BLM and very beautiful. Again you arfe not likely to see anyone else. About 6 miles from Glendas is unmarked BLM river access you can trailer into if you're non-commercial. About 7 miles from Glenda's is an excellent BLM campsite near Bull Gulch SWA called Jack Flats. There's a big eddy, plenty of trees for cover, and good hiking up amongst the Bryce Canyon-like hoodoos.
The next river access is off of Red Dirt Creek road, you can't get a trailer down into the water but can get very close for a short carry. The last access for a good long stretch is at my place, I live on the river and do float trips from Burns (info at www.confluencecasting.com
). I'll let people use my access for a reasonable price if you let me know in advance (we keep animals back there) and you're cool.
All in all, this is a very pretty section of the Colorado that pretty much flies under most people's radar. The section between my place and Cottonwood Island is very slow and can be hell with the afternoon winds. The lower section between Cottonwood Island and Dotsero sees plenty of traffic but is fairly boring. I'd recommend doing State Bridge to the campsite just below Catamount, then running the next day to Red Dirt.