From the sounds of it - some people's definitions of "hunting" Bison vary quite a bit from other people's.
Oh sure, if you are driving up to the tame ranch bred animals who are used to people and vehicles to "hunt" them - then I'm sure a 25-06, .270 etc. shot into the ear hole or eyeball will do just fine.
But if you REALLY want to HUNT Bison (Northern BC or Northwest Territories) then such talk would be foolish. They are much bigger than a Cape Buffalo - and wounded ones have been known to stomp people pretty good. They have huge lungs too.
In B.C. it is illegal to attempt to hunt Bison, armed with anything with less energy than a 7mm Remington magnum shooting a 175 grain has. Such a law was enacted after a few people hunting them became part of earth, in a manner they'd never imagined. I'm sure the thought of joining the "circle of life" looses all appeal when it actually happens.
I've seen them wild up there - and the herds were as spooky as any wild herd of elk on the planet. When they stampede it's a sight too.
Personally, if I were really "hunting" wild Bison, I know I would be carrying one of my 30-06's with a big "penetrating" bullet like a 200 gr Barnes TSX, or a 220 gr Nolser Partition, or my 7mmSTW with either of those makes of bullets in 175 gr - or something bigger. A big, wild, mature bull Wood Bison is bigger than any Moose, and it has a lot more "attitude" when hit - or so I'm told.
I know a lady outfitter (a native) from the Sikanni River country who has shot a mature Bison bull, once a year, since her youth, and takes people on Bison hunts every year - and she has hunting tales that "can make a man's blood run cold" - to paraphrase old Robert Service.
One tale she told, was about a "know-it-all-city-slicker-hunter" who was charged after wounding a big bull with a smaller than optimum caliber - with great laughter she described how the area they picked him out of looked like a "strawberry snow cone", as he'd done so much bleeding - he turned a wide swath of snow red as the bull tried to grind him into protoplasm. It was funny she said because he was relatively unharmed due to the depth of the freshly fallen soft snow - and but for the blood, and the screaming, and the torn clothing, he escaped with only his pride seriously wounded - when a bullet to the brain finally stopped the Buff.
But, I don't know how they hunt them in Nebraska. Perhaps Plains Bison, particularly farm animals, are different.
