Hey that's a fun loop. I'm sure you know what you're in for going from Baldy to Iron to Fish Fork..."fun".
Depending on your shelter, maybe all you need is a small bivy spot and no fire. If so, then you could probably find a suitable place near the bridge as the river often has small, sandy beaches along its banks. Poach yourself a night right on the bridge itself, done! Of course, if you need room for a whole tent then you may have to go a bit further down toward the trailhead, but not far, about a mile down from the bridge.
Have fun, hope you can find time to post up some pics/notes when you return.