When we rode to Alaska, we encountered bear almost every day after crossing in the border at Montana/Canada. Many mornings, we would wake up and find bear prints in the dirt around the tent. I was usually the first awake and would scrub the prints out of the dirt before Sally got up.
In McCarthy, we rode up the singletrack out the back of the mine, to the glacier. We checked out the glacier and on the way back down the trail there was a black bear and her 2 cubs in the middle of the trail. We were 2 up on a BMW R1200 GS. Maneuverability is not one of the traits. I kept riding toward them, honking the horn and revving the bike. The cubs jumped over the hill. Mom stood her ground till we got within 5 or 10 feet away. I was going to hit her if she did not move, I was not going to give her the first chance to attack. She dove over the bank at the last second, I could see her peeing while she ran away.
I think one of the more scary encounters was a bull moose in our camp during a trip up the CDT, in Wyoming. We camped in an abandoned national forest service campground. Early morning, we are making breakfast. This thing wanders into camp. Looking up at an animal, with antlers that are 5 feet wide, was very interesting. It eventually took off, I don’t know how something that big can run through the woods silently. It was spooky.