First off, quit yelling. We can hear you.
You're right about the Battle of Yellow Bayou not being on Yellow Bayou. The battle took place about two miles west of the bayou, and stretched from Bayou des Glaises probably to somewhere near the new highway, maybe a little beyond. If you go down the highway, you'll notice a lone tree standing out in a field. That big wide open field is pretty much the battlefield.
Next, who do you mean by "they." The Yankees? They crossed the Atchafalaya somewhere near where the new bridge is now, but the river was much narrower then. As to travelling by foot, if they didn't have a horse, they did, and most of them didn't have horses. From Hamburg, they followed the old highway/Bayou des Glaises down to Simmesport, crossed there, then marched up the far bank of the Atchafalaya to Old River, then on to Red River Landing on the Mississippi, and from there down the river to Morganza (those who didn't go up to Vicksburg, anyway).
There's one good map of the battle that I've seen, but don't remember the source right off the top of my head. I'll see if I can't find it in the next few days, if someone else out there doesn't beat me to it. There are several bad maps of the battle, watch out for them. Probably the worst source of information on the battle is on an old Highway Department map from back in the 60s.