I've been along on a bison hunt before. Saw one taken with a 7mm Remington Magnum, and the other with an old-school 45-70. The first thing to consider is shot placement. The bison taken with the 7mm was shot high and forward, in the neck/spine (as instructed by the guide). Dropped it clean, and they put three more rounds into the neck/spine area to finish it off. The other was shot right behind the shoulder with the 45-70. The thing didn't flinch, just ran off with the herd. Followed the herd and picked out the bull as he was dripping blood. Watched him for more than 60 minutes and he never seemed to even notice he was losing blood. Finally had to get close and shoot him two more times high in the neck/spine area, which dropped him both times, but he got up both times as well. Finally he laid down and we walked up on him and put a few more into that spot to kill him.
They are tough animals. While a bow shot can kill them, I'm not sure if you want to track a slightly wounded bison across the Book Cliffs. I know someone that got to shoot one with his Muzzy (cow tag) a few years ago. Solid hit in the vitals (like you might shoot other animals) and the thing bled for more than three miles before the blood gave out. He never saw her or the herd again... tag soup.
I'd recommend having a rifle very close by, even on your shoulder while carrying your bow. If one gets close without being in archery range, I think I'd be taking it with the rifle.
Congrats on an awesome tag. If I see the bison out there while scouting my deer hunt, I'd be happy to point you in the right direction...
"Therefore, wo be unto him that is at ease in Zion!" 2 Ne. 28: 24