Paying money to shoot a domesticated bison so you can eat it sounds okay.
Paying money to shoot a domesticated bison so you can let its body rot in the field while mounting its head in your den as a sign of some sort of accomplishment is ridiculous.
Is there such a thing as domesticated bison?
Domestication is a deliberate evolutionary distinction implying controlled breeding efforts by humans for the purpose of suiting humans. When humans domesticated wild rams we selected those with the sweetest temperment and the best wool production while deemphasizing things like horn size. These sheep traded their cunning and survival instincts for an easy meal and the protection of humans. This domestic species would do every poorly if it actually had to compete for survival in its environment.
Simply putting an animal in a cage, even if it is sweet and loving and nice, is not domestication. These are tamed wild animals, not domestic animials. Conversely, its possible for an otherwise domestic animal to break its bond/need for humans; we call these feral animals.
I have a pet bird and try to explain to people that unlike dogs, he is not a domestic pet, but rather a tamed wild animal. He has not been selectively bred through generations to learn how to relate to humans. If you want to be friends with him or any exotic bird, you have to meet him halfway and accept things like screeching, biting, and exploring because these are beneficial behaviors for the wild species.
However, there have been experiments demonstrating that when done right, it is possible to domesticate a wild species within a surprisingly small number of generations. Has this been done with the American bison? Just curious.