Gotta tell ya. I'd do it in a heartbeat! Especially in a large (as you said)fenced area.
But I'd have to say this is the ONLY animal I would hunt that way.
Why, because unless you pretty much hit the lottery, there are not free ranging Buffalo that can me hunted.
Buffalo hunting is part of the American Heritage. And to take one with a bow would make it even more complete. For me - longbow.
If you really want to read something exciting, get the Book Hunting the the Hard Way by Howard Hill. First chapter (I believe) is about his Buffalo hunt on free ranging Buffalo in Wyoming, even then it was very difficult to get a permit. He did it on an Indian Pony riding full speed shooting his longbow.
I've done it. It's tougher than any of these guys can tell you even in a large 1200 acre high fence area or larger. And no these animal will not let you get close enough to pet them. Be very aware they can kill you especially because they are herd animal with the instinct to charge you in a group. They are very aware of you before you can close the distance.
Shot placement is parimont as usual anda heart shot is the way to go with your first arrow. Their lungs are as big as a compact car's doors and it takes a long time to kill one from a double lung shot. I would say any fixed blade broadhead will do and any arrow with 425 grains or greater will do just fine with 200 plus fps. I'd be pulling close 70# as possible and still keep your accuracy up there.
Which bison species are you taking?Wood or plains? Bull or a cow? The wood runs a bit smaller around the 1200 # and the plains can go 1800 or more. The meat is super and take some pictures.
Best of luck to you!