You have two different things going on at the same time. In my mind Bears are raiders of opportunity and are just following their noses to a possible meal. I've only had a few Bear encounters, so I'm far from an expert.
I've had more encounters with Cougars and in your shoes I would be very afraid. They are ambush hunters and unlike Bears aren't really interested in your chow, they are interested in you.
A two year old Cougar freshly out on his or her own has a tough time, they get to the point it is either eat or starve to death. In other words they get desperate.
They can get way close before you are aware they are anywhere near. I can think of at least two incidences where my dogs didn't even know they were there, the Cats came in down wind for a look see.
Imagine a 100-150 lb. Cat crouched under some brush waiting for you to walk by. Or watching you from a berm or a bank on a Creek. Chances are if they are in the area they have already been close enough to you to hit with a thrown rock and you didn't even know they were there.
One instance that still makes the hair stand up on the back of my neck. I was exercising a couple of my dogs and happened to glance down a bank into the brush maybe 40 feet away and saw a Cougar there. That Cat was just crouched there watching joggers run by, it was a fairly heavily traveled fire trail, not far from some houses. Both of those dogs were Cat/Coyote dogs and neither of them alerted on that Cat. If the Cat hadn't twitched an ear I would have never seen it.
I'm from the it is better to be safe than sorry school of thought, either have a designated guard while you are working, get a big dog with a good nose or leave until it rains and the prey numbers improve.
I had one of my dogs get her stomach opened up by Cougar. We where running Rabbits near a little water seep in dry country. I was totally unaware of what had happened until I saw the Cat running away with my dog chasing it with her intestines dragging the ground. The whole thing went down in near total silence. I didn't hear a thing until the Dog went nuts and started singing as she was chasing the Cat. Best guess is the Cat had ambushed the dog and she put up a better fight than the Cat expected. Darned Cats don't growl, yowl or do like in the movies and make some sort of hubbub before or during an attack, they are silent killers.
One of the few places I keep a round in the chamber and the flap opened on my brush holster, is in Cougar country. And even then I most always have a dog with me and no big expectations of seeing that Cat until it is right on top of me. That Cat likely knows when it is within a quarter of a mile of you, you are at a distinct disadvantage.