Just to follow up on this, from a recent similar experience...
My wife and I were out elk hunting, perched above a nice little natural spring, near dark, waiting for something to show. Over a little hillock, I kept hearing a squirrel screaming at something. Usually they are screaming at my clumsy butt, but not this time. Anyway, a big mountain lion comes over the hill toward us, about 30 yards. I have a 300 WSM pointed at it, so I am not particularly scared, but my wife is getting itchy. Finally, she jumps up and screams "holy fuck, holy fuck it's charging and it is going to kill us." Of course the cat turned right around and ran away. Point being, other than grizzlies, there aren't many animals out there that are going to mess with a screaming crazy lady, so unless you really want to hunt one of them, let them go on their way. They aren't likely to hurt you. Doesn't hurt to have a gun pointed at them in case they are wrong in the head, but most predators are pretty cool animals.
BTW, this is a 100% true story from about 3 weeks ago. She won't live it down for a long time.