A few years ago I was walking in the woods in western Washington state (USA) the forest was Douglas fir, with undergrowth ranging between 2 and 10 feet high (1 - 3 meters). There was no trail.
I was trying to be quite as I was hunting squirrels with a 22 rifle. The area I was in had brush about knee high.
Suddenly a short distance in front of me I heard a lot of noise in tall bushy area. Three black bears came storming out of the brush, running in different directions. I was standing about 2 feet from a tree, and I side stepped to get behind it. All three where different sizes, I don't know but I think it was a mother and two grown cubs of maybe 2 and 3 years old.
One went well away from me and the other two came in my general direction. One bolted between me and a nearby tree. The last was running nearly directly toward the tree I was hiding behind. At the last moment it choose a tree just to one side. It went up that tree at the just about the same speed it was running through brush.
The one in the tree only went about 20 feet up and stopped, I could still hear the other two running through the brush. A few moments, it was quite, my heart was racing and I was scared. I moved away from the area, in a direction that bears did not go, slowly until I had some distance between the area of excitement and myself. At which point, I ran.
The choices I made may or may not have been the right ones, but I gained two sure points of knowledge.
- A black bear can climb a tree, faster than I can. In fact from the time we became aware of each other, I could not have climbed 20 feet up the tree nearest me.
- If I had stepped in front of the tree, and that bear had decided to climb my tree he would have gone right up me and then the trunk of the tree.
Point 2 is important, because the first two things that went through my mind were; I have a 22, this not a viable weapon for a bear, followed by, I should stand in front of the tree to hide my silhouette, so I can keep a better eye on what is going on. All of this happened FAST, I didn't actually decide to step behind the tree it just happened.
My answer to your question "Will Black Bears actually follow you up a tree?" is 100% yes, they will climb right over the top of you to get as far up a tree as they can so you can't get them. When you and a black bear become aware of each other, do your very best to stay out of his escape route.