Step one: put your net in your pocket
Having your net in your pocket will help you make sure that you're prepared to act quickly when there are bees to catch.
Step two: go around shaking trees
Continue shaking trees. You will eventually find one with a bee hive in it.
Step three: Run away and make the bees go off course for a moment
As soon as the bee hive falls, start running. Then, when the bee swarm gets really close to you, quickly change direction. If you time it correctly, the bee swarm will keep going in the direction that you had been going in before, and then they will briefly stop. As soon as this happens, go into your pockets.
Step four: Equip the net and catch the bees
While in your pockets, equip the net as quickly as you can. You only have a moment before the bees start chasing you again. Once your net is equipped, exit your pockets and watch the bees very carefully. You should be able to turn and face them and catch them with the net. If not, run away and change direction again, then catch them as described.