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.
When following the Giant Queen Bee its good to have a full set of ghillie armor, bug repellant and for some reason crouching seems to put you slightly below the drones hit range, as long as you keep moving that is. I used this tactic earlier today to tame my first queen and it worked very well
They spawn on Redwood trees, always lvl 5, break the hive with a flyer, the queen should drop on the ground, bring ghillie + bug repellant, you need 2 ichty kibbles or 5 flowers, the queen seems passive but the bees will attack you. Once tamed you can convert the queen into a hive (structure) it produce 1 honey pot per hour (not sure)
Sometimes when the hive is destroyed the queen will just fly in place. If you have a quetzal or a Tapejara you can fly up to it and passive tame it right there. I recommend bringing medical brew just so you don't have to worry about the drones. Make sure to feed your tame bug repellant as well.
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.