IMHO, if it can be reasonably done with a .30 caliber bullet, a .30/06 can do it, when you need more, bigger is better than faster. Faster is great when the thing you want to shoot lies beyond 500 yards, but out to a quarter mile or so, the '06 does pretty well if you can shoot. If you can't shoot, it doesn't really matter what lies in the chamber of your rifle. If I was going to hunt bison with my '06, I'd load it with 240 gr Woodleighs, which is also the bullet I choose for the '06 when I carry a light rifle for bear work.
If the opportunity for bison came my way, chances are I'd select either my .375 or my.458, as I am not a minimalist when it comes to cartridge selection, but the flip side of the coin is how much recoil and blast can you tolerate, and from which positions can you tolerate it? If all you can do is shoot your rifle off hand, then IMHOI, its too much gun for you. A hunter should be able to shoot his general purpose big game rifle competently from all field positions, including prone. A hunter doesn't have to shoot a string of 20 rounds from prone, but he should be able to tolerate 3. If he can't do that, he has too much gun, except when niche rifles are used for elephant or African buffalo hunting in long grass where the action is fast and the range exceedingly short. I believe the correct answer is to hunt with the most powerful rifle you can shoot well, and that you should develop basic competence with that rifle prior to going afield. When attention is paid the the fit of the rifle to the shooter, the choice of a suitable recoil pad, the correct choice of optics and mounting, shooting well in the field is easier.
Some jurisdictions have minimum caliber or minimum energy requirements for some species of game. Many, if not most African countries, demand a minimum of a .375 for buffalo, but will accept a 9.3X62. The Yukon requires a minimum energy of 2800 fp at the muzzle in order to be legal for bison, and this is based on the .30/06 180 gr factory load which the Yukon Government uses as a baseline. I doubt if the bison is killed at the muzzle, but trying to establish an energy figure at the target would prove too convoluted to be understandable in regulations. By increasing the bullet weight from 180 to 220 or 240 grs, that baseline is easily exceeded with the same .30/06 rifle.
As for a rifle recommendation, a Ruger 77 Hawkeye might be the best bang for the buck at this time, although I detest what they did to the Ruger Alaskan. If you can afford a Cooper or Dakota, or for that matter a Kimber in one of the fine wood models they offer, let personal preference rule. I have a soft spot for old Brnos myself.
