American bison are the largest land mammal in North America and the most complicated game animal on the continent to talk about honestly. The species was reduced from an estimated 30-60 million animals to a few hundred by the late 1880s, recovered to roughly 500,000 today, and of that total only a small fraction — somewhere on the order of 20,000-30,000 animals — are managed as free-ranging wildlife rather than as livestock. The IUCN lists Bison bison as Near Threatened because the wild-population genetics, not the headcount, are the constraint.
Huntable populations open to public draw are therefore narrow. In Montana, the hunt is the Yellowstone-area migration boundary outside the park — managed jointly by FWP and tribal nations to keep brucellosis out of cattle herds. In Utah, public draws exist on the Henry Mountains and Book Cliffs herds, both descended from Yellowstone stock. In Arizona, the Raymond Ranch and House Rock Wildlife Areas hold huntable populations. In Alaska, the Delta and Farewell herds are drawn through ADF&G. South Dakota has a Custer State Park hunt, and a handful of national wildlife refuges (Wichita Mountains, others) run intermittent reduction hunts.
Anywhere outside these specific units, what is offered as a "bison hunt" is almost always a fenced or commercial operation on private herds classified as livestock. That is a different product and worth being clear about. The wild-bison hunt, where it exists, is one of the lowest-odds draws in North America.