I've probably hunted the Unlimited Sheep units as much as anyone. Not only with a sheep tag in my pocket but also in them hunting a mountain goat, elk, and moose. In all the years that I hunted in those units I only encountered 2 bears, one black and one grizzly. Both of those encounters were one year when we were camped at the end of a FS road and we had the quarters of 2 elk and a moose hanging in the stock rack in the back of my truck. I respect bears, but I don't worry about them.
Success in killing a ram in an Unlimited unit is very low with a rifle and even lower with a bow, but it can be done.
One year I was hunting rams moving up through the timber adjacent to a wide avalanche chute. I had my Golden Retriever with me. About half way up the mountain I came across two legal rams in the edge of the chute and close enough that I picked up a golf ball size rock and threw it underhand and hit one of the rams. I had already killed two rams in previous years, and the year before I had shot a full curl ram, so I wasn't interested in these two rams.
When my rock hit the ram they both ran up the avalanche chute where a guided hunter shot one of them. The shot was low and back in the belly and the rams ran back by me where they split with the wounded one running deeper into the timber and dragging his intestines like a rope. I didn't want to see him suffer so I followed him into the timber and killed him. I then went back and found the hunter and guide and took them to their dead ram.
When I first saw those rams I could have easily killed either of them with an arrow. I did go back into that unit the next year and shot the other ram.
The last time that hunted sheep in an unlimited unit I was hunting with my son and again, my Golden Retriever was with us. The day before the season opened, I saw a great full curl broomed ram below us in the timber. On opening morning that basin was full of hunters and their camps and I never saw that ram again. But my son, dog and I did get close enough to a bunch of ewes, lambs and young rams that we could hear the sheep biting off the grass that they were eating. They were definitely close enough for a bow shot.