When two bees are bred together, the resulting offspring randomly chooses one race from each parent (baring in mind they've got two racial traits to pick from from each parent - active and inactive). For example, if you breed a demonic bee with a excited bee, the result will always be hybrids. Breeding those hybrids with each other gives a 25% chance of getting a pure demonic, a 25% of a pure excited, and a 50% chance of another hybrid, per offspring.
Mutations mix this up a bit - instead of getting a trait from the parents, if it's possible to mutate then you might get the mutant set of traits instead. Early on, breeding with soul frames is often enough to get both active and inactive sets of traits to mutate fairly often, but this starts to change with later generations of bees.
If you want to get anywhere, aim for imperial bees - these give you the resources needed to build the genetic machines from extra bees that'll make things a lot easier (and along with industrious bees, the resources to make alvearies, which'll greatly increase the output of ALL your bees).
Minimising lifespan and maximising fertility is essential to getting the dice to roll in your favour.