I go on longer runs where I may not see anyone for several hours. I almost always have my bear spray. In some areas, I hold it in my hand as I run. Most of the time I am more concerned about tripping on a rock and busting open the bear spray can and making a big mess. Until last year...
On a pre-sunrise hike in July, my son and I were headed up the trail. I saw a branch right along the side of the trail wiggling pretty hard. We were about 15 feet away my son pulled out his bear spray and we stopped in our tracks. The bear jumped up and rambled away thankfully we scared it.
On another afternoon in the fall, I headed out from downtown Jackson up a canyon. I was wanting to do a trail I’d never had the time to try. It was 4 pm and there was lots of people in the area. I headed up the trail and the brush was thick so I kept my head on a swivel. Sure enough, I hadn’t made it a quarter mile and saw a bear. I was safely distanced but it was clear the bear was headed up the same way I was. I opted against following it.
In reality over the last 40 years there are a lot more bears. My FIL worked for the Forest service and planted trees all over the BTNF. There are some really great areas. He found countless fishing spots, but some are just too dangerous to go into any more.