I think of it that way:
Breeders:
Lay eggs. Probably they once did more, but now they do not have to do all the hard manual tasks anymore.
-Nursers:
Care for the eggs and do genetic experiments with them (so they have two functions). Makes sense because it's easier to have a bug that is a dedicated evolution booster than reduce the breeders breeding capacity for this.
And also it is already the nursers job to care for the eggs and have a look at how they evolve, so it fits.
-Queens:
Well, as said they rule worlds.
It would make sense for a queen to lay eggs, as long as it doesn't reduce her capacity to rule their colony.
So a queen only makes sense in a big bug colony. There needs to be a logistic system to provide her with food, breed all her eggs and defend her.
As it is already most valuable (it's the bug emperor) so why not have it lay eggs? You already need to defend it at any cost, so making it a little more important doesn't make it any more problematic.
At least you can asure you have a REALLY great number of bugs around her.
-Drones
As said I prefer the Termite way for bugs (different but similar looking sexes across all casts). Question is - where are the drones?
If a queen ist really such a factory bug there are some different ways:
-Drones are only bred sometimes, have sex with the queen and then dissapear quickly (sheet louse model).
-Drones can be found all the time in arachnid hives, but only in the queen's chamber (Termite model).
-Drones are IN the queen bug. They bite it and then mold together for eternity, sharing even one blood circular system (sp?) (deep sea fish model).
-Drones just consist of a sperm delivery organ, some sensors and rudimentary legs. They do not have any big legs, claws, no mouth or a digestive system. When they hatch, they are taken by nursers, brought to the queen, have sex and die instantly (parasite trematod model), probably even during the act, like bee drones.