Where a ghillie suit and use repellent if available. Once your break the nest the bee will fly to the floor and start spawning in baby bees. Try to quickly feed the bee then back off because her spawns will attack. Watch which way the bee goes! Since they have a small radius to be seen let it go out of view and it'll reset how many baby bees she has floating around her, that's when you run in and feed, then repeat.
If you want to tame one, the easiest way is to get a dire bear and break the nest, because they are immune to bees. Use it to break the nest, then when the nest beaks, make sure you have full ghille armor and bug repellent, and tame it with simple kibble. You can then go to the bee and press the 'aquire nest' button, and it will give you a bees nest. You can place this on any natural ground, but no human made floors. Put rare flowers into it, and it will produce giant bee honey over time. Rare flowers can be harvested from plants in the swamps across the island, but beware of the creatures that dwell there. When you go into your bees nest to gather honey, you will get the bee effect and start taking damadge, even though it is your own bees nest.
ALWAYS break the hive with ranged attacks. If you choose to melee it,drones will continuously spawn from it infinitely, and they will repair the hive, so best to shoot it down and kill all the drones before attempting a tame. Oh, and the queen will spawn more drones periodically, so bee careful.
2021- tried several times with past tips/videos to tame the queen bee. Such a nightmare lol. Only thing that worked was breaking the hive with my dire bear, eating a bug repellent, then crouching below the queen bee with regular kibble in my 0 slot. Finally worked!!