Just last year I had two encounters in August & September. One where I was out for a scouting hike with one of the kids and an average size bear walked out onto the trail 35 yards in front of us. Bear was surprised to see us. Gave us the once over and took off running within 5 seconds. The second time I was working on a tree stand for deer season and a bear was hanging out just out of sight in the woods. I yelled at it to go home (meanwhile I'm the invader) a couple of times and it did. On the way out I noticed it had been turning over rocks looking for grubs.
I didn't have a firearm either of those times but the second I had a bear tag in my pocket I couldn't find a bear. If you are worried about bears just buy a tag and you won't see one ;-).