How many bee Queens are there in a bee hive?

Under normal circumstances, one.

When the queen is getting old the workers will build queen cells and produce new queens. The first one to hatch will go round the other queen cells and sting through the cell wall to kill the developing queen inside. For a short time there will then be two queens and it may be possible to spot both the mother and daughter queens on the combs. Once the daughter queen is laying, the old queen is killed by the workers. This is a process known as supersedure.

When preparing to swarm, the workers will again build queen cells, but before the new queens hatch off, the old queen and roughly half the colony will leave, so for a short time until one of the queens hatch there will be no queen in the colony.