The first bee you want to make is the Common bee, which is made by breeding any two hive bees together (for example, a Meadows Princess and a Forest Drone). Be sure to analyze any cross-bred bees you make. You want to try and get a pure-bred (i.e. Common-Common, Princess and Drone) going before continuing. You also want these Common bees to stack so this means that you have to breed a few of these bees. Some will die off and some will be no good but keep using the Analyzer.
The easiest way to accomplish this is to put a Forest Princess (or Drone) and a Meadows Drone (or Princess) into an Apiary. The work meter will go up, and once it’s complete, the Drone and Princess will be replaced with a Queen. This queen will work and eventually die off. Once the queen dies, she will leave behind a new Princess (Ignoble have a chance to not leave a Princess, but only after a TON of generations) and a new Drone (it could be more than one; this is dependant on fertility).
You want the queen to leave behind a Common - Common, a purebred Common Bee. This will make it easier to progress to the next bee. You want these new Drones to stack (this makes it easier to automate). Keep breeding these Common - Common bees, as it's always good to keep a reserve. It's also good to have pure hive bees breeding; used to purify a bad princess with spare drones. This could take a while so you need to be patient.