I never thought I'd say this, but some parts of the game is not convoluted enough, and one of them is beekeeping.
First: How do we aquire bees?
In the game by making a bee skep. For some reason the bees magically appear in the skep.
In real life that would almost never happen. We there fore need wild bees whom we must "harvest" by knocking them into a container, a skep for example.
Next we could breed the bees from already exisiting tame hives. We could do this by removing the beequeen with some other bees to a new skep.
The old skep would then hopefully create a new queen. (Chance of failure should be pretty high, maybe 30%?). We unfortunately do not have access
to modern equipment such as the Langstroth hive with frames.
Second: Honey and wax production.
Honey is derived from flowers and some plant juices other than flower nectar. The flow is best if there is a mix of some rain and alot of sun/warmth.
Weather should be introduced to make beekeeping more interesting. Prolonged dry weather/sun would halt the production of nectar. Cloudy/cold/rainy days
would also stop the flow of nectar. Wax takes alot of honey to be produced. Therefore the bees use most of their honey to feed on and build wax in the beginning.
Honey production should be slow in the beginning and depend on the weather as stated above.
Third: Harvesting.
In the olden days with beeskeps the wax was destroyed to aquire the honey. Every time we harvest wax/honey, the entire operation would be set back to almost scratch.
Most of the wax was removed and strained in a sift or cloth or something like that to make the honey purer.
Fourth: Storage.
You can not store honey in a bucket for a long ammount of time. Honey is hydrosopic and attracts water from the air. Over time the honey will be watered out
and start to ferment, creating the drink of the Gods: MEAD. If you want to keep honey as honey, you need to keep it in an airtight storage.
If you have any more questions about beekeeping, please ask.

Also: If you try to harvest/rob a hive for honey you will most likely evoke a violent and merciless reaction from the bees.
A human beeing is likely to die or be severly debilitated even if not being allergic.
Here is a bear that is designed to withstand bee attacks:
https://www.youtube.com/watch?v=YJ42pMtmrlE