Bee stings are unpleasant to say the least. However if you are after a bumblebee you will have to shake some trees and do your best to get out that net in time.
A lot of times you will just get stung. You won't be able to catch the bee and you will end up with a hurt face that everyone in town will make fun of.
So what to do? Well first off be sure to buy accident insurance. If you have insurance you will get 100 bells everytime you get stung, which eases some of the pain. Next there are two ways to get rid of a bee sting. The cheap easy and quick way and the expensive easy and quick way.
You can either buy some medicine from Tom Nook or you can save your game and restart. Either way your bee sting will go away and you will still get the 100 bells.