I have never hunted bison, but I went along and watched as a friend of mine shot one. The stalk was unnerving, tension-building, and we wondered if he would get away alive . . . no, just kidding. I watched as my friend ran down a gully about 1/2 mile to about 150 yds from the bull, then eased up over the edge, placed his rifle, and fired one round. The bull turned around, stood there about 15 seconds, then the front legs went down and planted his nose in the dirt, back legs still standing. About 30 seconds later, the back end collapsed. We all walked down, slapped my friend on the back and high-fived, and walked up to the bull. His mouth and nose were full of blood, the entrance wound was right above the elbow and there was no exit wound. The ranch hands drove up in a truck and hoisted the bull in the air, then drove him over to the concrete slab a mile or so away where they gutted and skinned him.
The heart and lungs were annihilated, just puffy and shredded. We did not find the bullet, but it penetrated the chest and did its job. The rifle was chambered in 243 Winchester, not typically considered a buffalo-hunter's round. My point is that although it might be fun to buy a 45-70 for nostalgia, any good deer round will put one down.