In A Nutshell
Besides having one queen bee, hives also have multiple virgin queens who will kill each other off in order to be first in line to succession. Failing this, they can become the queen of their own hive by mating with drones outside the nest.
The Whole Bushel
Everybody knows that hives have a single queen. Only she is allowed to breed with drones (male bees) and reproduce. However, the queen can also lay multiple queen eggs. These baby queens are fed royal jelly (the stuff that creates queens) and sealed inside cells. When they hatch, they can either take flight and try to start their own hive or they can take a more Shakespearean route and kill off the other virgin queens littered throughout the hive.
They’ll do this by exiting their cell, finding the other virgin queens, and stinging them to death through the cell walls while they’re still asleep. They have to be quick about it, though, because while they’re killing off their sisters, there’s a chance that the original queen is creeping up behind them ready to go all Game Of Thrones on them. However, if they do manage to kill their way to the top, they can rule the hive and mate.
However, if they mate while the original queen is still in the hive, she will give off a pheromone which causes the other bees in the hive to attack and kill her. If she survives long enough to do so, a virgin queen can become the queen of her own hive through another grisly route. To do this she will will fly off during swarming season, locate a swarm of drone bees and then release a pheromone to attract them. The swarm will instantly pick up on this and begin to chase the queen. The first few drones to arrive will be allowed to mate. However, unluckily for them, after the act of mating their sexual organs will explode at the point of climax. Once impregnated in this way a virgin queen can settle a hive of her own.