Last year in the Uintas, they were requiring everyone to hang their food. I am sure that is the requirement this year as well. There are definitely black bear there, although I have never seen one there. There are also rumors of a few grizzly that wandered in from Wyoming. The Wasatch and Uintas are filled with cougars and moose. I am more scared of moose than cougar. I have seen cougar tracks in the Uintas, but never a cougar. I have only seen 2 moose so far. I always bring bear spray.
Having a fear of animals is natural. Just don't let it consume you. Practice safe animal avoidance techniques, and you will be fine. I think bringing a dog helps in this regard. Usually people stop worrying about it as they gain more experience. If you need to always bring a friend, then I would say do it.
I've taken a vow of poverty. To annoy me, send money.