My post about the .25-06 was of course meant to be somewhat humorous--but is also absolutely true.
Hunting bison can indeed take various forms. My friends in Alberta who hunt wood bison that stray outside Wood Buffalo National Park (which straddles the Alberta/NWT border) tend to use the same rifles preferred by Cape buffalo hunters. These are wild bison and sometimes charge seriously. Since much hunting takes place in winter, with the hunter up to his knees in snow, stopping a charge is very necessary, since running ain't an option. The .375 H&H is considered a decent minimum, but some use hunters use .416's or .458's.
I have only shot one bison, an eating-size bull in mid-winter that, as Mark described, took about three minutes to die. The rifle was a .375 H&H with 300-grain Nosler Partitions, and shooting him twice (both times fatally) did not speed things up.
That was a meat shoot, plain and simple. The rancher told me that how long they take to die depends a lot on the season. In winter, apparently, their metaolism slows down so much that it takes longer. In summer they die quicker.
I have seen quite a few other bison shot. The quickest-deadest from a chest shot was a mature cow my wife shot in Texas in warm weather. It was actually an interesting hunt, as the cow was in fairly thick thornbrush, and had shown some aggression when her brother had been killed a few days earlier. Eileen stalked her for 2-3 hours before getting just the right shot, and put a 130-grain Triple Shock from a .270 through both lungs just above the heart. The cow went about 40 yards and keeled over within 20-30 seconds. Live weight was around 900-1000 pounds.
I have also seen bison taken with traditional blackpowder cartridge rifles and they do about as well as anything on heart-lung shots, as long as the bullet has something of a flat point, is heavy enough to penetrate, and is put in the right place.
If I ever do it again I will either use a .25-06 (when slaughtering one for meat) or on a real hunt, something much bigger.
I also once helped field-butcher a cow bison with stone tools, which was actually a lot easier than it sounds--and was a lot more efficient than many of the "modern" field jobs I've seen.
