The first time I did Kings Peak, I also thought that Elkhorn crossing was where we should go. Since so many pack animals use the Henrys Fork trail, they have people use Elkhorn crossing since horses on a footbridge might be dangerous.
Last year near the end of October, the bridge was in somewhat poor shape, with something like two logs still holding together, and a third log a foot or two away.
This year (Sept. 17, 2004), the bridge had been renovated with more logs. This time, it had at least five logs across. Very luxurious! There is a sign in the middle of the Henrys Fork trail before you hit Elkhorn crossing. If you are looking down at the rocks (if it is dark, it is easy to miss so watch it!), you may not see it. I've also seen people crowded around the sign, blocking its view a few times as well. Anyway, from the sign, turn left and watch for a path that leads in the opposite direction of the trail up to that point. It will head downhill towards the footbridge.
I also noticed that somebody has placed small reflective dots on the trees that head down towards the bridge, should you do this at night with headlamps.
I believe the footbridge is approximately 6 miles from the Henrys Fork TH, and at least a hundred feet or so before Elkhorn crossing.