I see someone at the National Parks Service has a sense of humor. They've released this handy graphic showing where on a bison it is safe to pet them.

As you can see... nowhere.  Each year lots of tourists forget that they are dealing with wild animals and they do really stupid things trying to get that perfect selfie. Usually with a bison. They look so big and cuddly, don't they? Us Montanans know better.  Those big beasts can run a LOT faster than you.

Tips from the Park Service recommends staying at least 100 yards away from bear and wolves and 25 yards for all other animals. They say that if your actions cause an animal to move, you are too close.  Common sense, I know.