Blue bear tells me to catch a honeybee but I don't know how. How do I..

First of all, whatever he gives you for doing probably won't be worth the work, but, here goes...
#1 - Shake trees.
#2 - Eventually a bee's nest will fall out of a tree.
#3 - Press Start and get out your net.
#4 - Catch a bee!!!
(Please Note: I am not responsible for any bee stings you may get if you don't catch the bee(s))

Warning i have the wii so i may say press plus, minus, a, b, c, z, etc. i never personally caught a bee, it is very hard, but people have been telling me (people being my very very very close friend who had animal crossing for, like, EVER) to shake trees until a honeycomb falls out of one. its usually the third-fifth tree u shake. right b4 the hive hits the ground, hit plus or start, depending on if u have the wii or ds, i dont know the controls for gamecube, and get ur net. run really fast until u cant see the bees. when the bees are in sight, jam a really fast and u might have it in ur net. or u might have a nasty sting on ur face. it depends on ur luck.
hope i helped!

The way I've found most successful is to:

A. Choose the right tree! Make sure nothing is blocking your getaway, like rocks, trees or houses.

B. Equip your net so it's the first thing that will emerge.

C. Randomly shake trees. NOTE: You will be closer to getting a beehive AFTER shaking out bags of bells a few times--but then again, you may get a hive right away!

D. As SOON as your character can move, RUN (to the side, not up or down)! Go a short distance and hit "Pause". Equip the net.

E. As soon as the swarm of bees approaches, "unpause", and just as the swarm is a net's length away, SWING! Once the swarm gets too close, you're going to get stung!

It takes practice and fast reflexes, but it's NOWHERE as hard as catching a banded dragonfly!