With the latest update, you can hold your net while shaking trees. That way when a bee drops, you'll turn towards it automatically with a shocked face, and you can just mash 'A' until it works and ta-da! Bee caught!
For me, I still haven't caught the house centipede. It remains elusive. Tarantula and scorpions were oddly easy for me? I got them on the second and first tries, respectively. The first time I saw one it scared me half to death though, I didn't know they were a thing.