What I did was run straight up for a long distance, face downwards, and then the bees would come directly for me in a straight line and if I timed it just right I would catch it. This method worked for me in all games except Wild World. Let us know if you manage to catch the bee!
I like to shake the tree, run a little bit away, pull out my net, then i turn around and swing it when they get close. But dont run too far or theyll catch up. Its very inconsistent though, but its what works well with me!