The bottom of Bright Angel Trail follows the bed to the river. Just upriver from the mouth is where most rafting groups land to do their exchange. It's another mile to Bright Angel Campground crossing the Silver Bridge and an extra mile to follow the River Trail to the Kaibab and the old Black Bridge. Where the trail leaves the bed going up to Indian Garden is called the Devil's Corkscrew. This segment has been reconstructed and some of the original sections can be spotted.
Old photos are interesting to compare with the current trail.
It should be OK to continue up the bed and come out on the Tonto between the Bright Angel and Kaibab Trails.