The Queen Bee is a block that:
- can spawn by itself on any block of tree-leaves, except for palm-like Shorewood-trees
- will then grow into Beeswax if in a fitting environment
- or else can just stay Queen Bees in too hot or too cold biomes, on high altitudes or on/near the ground of Swamplands
- can often be obtained as an occasional additional emblement when harvesting Beeswax (comes with world creation and will continually grow additionally here or there on nearly every kind of tree except for Shorewood)
Placing blocks of (once already harvested) Beeswax on the ground or on Wood and picking them up again does not seem to provide you with any Queen Bees, different from the random additional harvest from Beeswax that has just grown on Wood or Leaves.
You can plant Queen Bees yourself to grow Beeswax from it.
Since R22 in September 2015 you cannot place blocks of Queen Bee just anywhere into the world any longer, but only on (blocks of) Wood, and (since R25) also on any block of Leaves again, except for (blocks of) Shorewood, Shorewood Leaves, Dark Wildwood Leaves, Logs or corrupted blocks of any kind.
Growing Beeswax is very simple currently, as you can just place Queen Bees on single blocks of Wood or Leaves that you placed within fitting environments and wait, like Cragwood, Wildwood, Ashenwood, Elderwood, Weepwood or Parchwood for example.
If the environment allows it, Beeswax will grow by itself into a "hive" made of up to max. 6 blocks of Beeswax that will replace the Queen Bee within ca. 3,5 hours (real-time). You don't have to be near for this; because Beeswax will also grow while you're offline.
Just take care not to plant Queen Bees (on Wood or Leaves) in too cold or too hot environments, neither on altitudes too high up nor on the ground of Swamplands.
In such environments Queen Bees will stay fallow (you will see this word written in red letters when taking the Queen Bee into your focus) and of course fallow Queen Bees will not produce Beeswax under any circumstances, but will simply stay Queen Bees.
You can plant Queen Bees close together (better not too close or less beeswax can grow the less free space they can grow into next to the Queen Bee), at least it does not matter how much Beeswax has already grown in the area, on surrounding trees or the like.
Queen Bees do not need any light to grow and such can grow well underground, even on the Corruption layer if planted on fitting blocks of Wood or Leaves (not corrupted ones). Only the Lava layer will be just too hot of course to let Beeswax grow, but it might also be unfitting as a Biomes itself no matter how much you can cool down the direct surrounding.
Queen Bees seemingly cannot be fertilized currently.
Other than that you can put Queen Bees into Wood Planters, Flower Pots and on Wall Shelves (all of which have their own inventory-slots to put items into). Queen Bees will not change/grow into Beeswax there.
Queen Bee blocks cannot be used for any crafting-recipes (as of R27 in January 2016).