If you have a drone which a common trait on it, then breeding that with your common/forest princess will give a 25% chance of getting a pure common bee per offspring. Assuming the drone's other race can't trigger another common mutation, in which case the chance is slightly better.
If you have a common/common drone to breed it with, then that becomes about a 50% chance per offspring.
If you don't have a drone with a common trait on it, then breeding most anything else with your current princess will give only a 50% chance of getting even another hybrid back, or a 50% chance of losing the common trait completely. Again not accounting for mutations.
Once you HAVE a pure common princess AND drone, then breeding them over and over will eventually give you a STACK of common drones. Breeding those with a given princess over and over will eventually see THAT become pure common too, no matter what race it started out as.
Once you have the genetic machines running then it becomes possible to directly change the race of bees without going through the breeding process (I once wrote a
bit of a rough guide, though there are plenty of others out there).
In the meantime, don't think small. Make more alpairies, run them all at once (throw lots of dice, not one!). Harvest more wild hives. Work out how to make soul frames faster. Don't be afraid to throw away rubbish drones (into a genepool preferably), but make sure you hold onto your princesses (whether you can use them now or not).