Polytheism / Swarming does happen within the colony under various circumstances.
If the colonies queen is getting old, or under performing as a queen (not laying properly or is a virgin) the bees will 'kill her off' and will under go supercedure, rearing another queen to replace her.
If a colony gets very strong in the peak of summer, and the bees think there is not enough space for them all, they will also under go supercedure, and half the colony will stay in the hive with a new queen, the other half will swarm and fly off with the old original queen.
All queens give off pheromones (a scent) which the colony can all smell and detect, no queen has the same scent, so the bees will know exactly who their queen is, and if you remove a queen from a hive leaving them queen-less - they will know within 15 minutes that she is not there.
The queen sets the temperament and performance of the entire colony - if you have an aggressive queen - you will have an aggressive colony, and vice versa. This is why having a good Queen in your hive is so important, to help you work together with the bees.
The female worker bees all have different roles / jobs in the hive depending on their age. The older worker bees tend to have the jobs in the hive of more responsibility, such as guarding and foraging. The younger bees tend to be the nurse bees which stay in the colony looking after the brood / young, the wax builders, and the cleaning bees which keep the hive clean and tidy.
The age of the female worker bee determines her ‘hierarchy’ in a way, albeit all the jobs are important and keep the colony running smoothly as a whole.
Throughout the swarming process a few bees are sent out as “scout bees” in search for a new place to call home - once they think they have found somewhere they go back to their colony and let off specific pheromones instructing the others where to go, then half the colony will break off and they will swarm to their new ‘home.’
Sometimes, if a hive becomes queen - less unexpectedly, or the queen isn't laying, a worker bee can become what is called a “laying worker’. However, because the female worker bees do not mate, they can only lay unfertilised eggs, which are drones. It is usually very clear to see if you have laying worker in the colony, as she does not lay neatly like the queen, and you will find a colony full of messy - erratic looking drone brood.
If you ever happen to be fortunate enough to see honey bees swarming in action - do not fear! When they are swarming they are completely un-interested in you, and are only focused on finding their new home. They will often hang in a tree or bush like I have photographed here - temporarily until they find a suitable place to set up home.