The bison in 26 are, and always have been, wild and don't respect international borders. But they are all on private land, so you'll need to get a "land-owner tag."
At the Amendaris between Socorro and TorC...Turners own web page (referenced above) lists the bison with the wild animals, not with the reintroduced critters. I'm pretty sure though, that if that herd is indigenous, that Turner has supplemented it with bison from elsewhere. They manage the bison like any other livestock herd, with some species-specific changes. It's gotta be like paying to go on a Black Angus hunt (for which you can probably also get a land-owner tag).
Here's some notes from a 10-year old article: The cull cows, generally about 20 years old, are harvested through hunting..."We just started removing the older cows," Wadell says... They've always removed their dry cows. "Now, with the drought," Wadell says, "we're dialing down a little bit. We're getting the numbers down to where we don't have to supplement."...While the livestock operation pays the bills, Wadell says he can see the day when the hunting side of the operation could be extremely profitable. Some of the culls are shipped and slaughtered, Wadell says, but they're worth more as game animals..."We've got a great market here," he says. "Same thing with our older bulls. I think last year we shot 188 cows and 38 bulls."...People come from around the world. Wadell says there's a waiting list for bison hunts. They get a lot of families who come out on a hunt..."It's like going out to cut a Christmas tree," he says. "It's a family recreational event to come out, and you've got buffalo meat for a year."
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