I don't catch bees often, but usually I start running as soon as the hive falls, then when I'm far enough ahead turn around and pull out my net, and wait.
I read a tip online about how to catch bees and I've used that method ever since. I run straight north of the tree and pull out my net so I face south, and then quickly swing as soon as the swarm of bees appears at the bottom of the screen! It usually works very well with the right timing, but I'm still a little scared of bees, so I rarely ever go looking for them, hehe.
I made sure the net was the only equipment in my inventory and used the d-pad. Then I'd shake the tree and run away equip my net and swing it at them. I'm terrified of bees IRL so once I caught one I never looking again.