Basically, how bees work with traits (not mutations) is through medelian genetics. there's a TL;DR disclaimer if you wish.
Simply put, with the traits of its parents, for each trait the parents have, the parent has a 50% chance to pass on the active, or inactive trait. This happens with both parents, so for each individual trait of the parent, the children bees have 25% chance of inheriting any one specific trait.
This makes trying to get common bees with fertility three tricky, saying you have a pure common and pure forest bee to start off with, it has a 25% chance to come away with the traits 2x, 2x. 50% chance of coming away with 2x, 3x. and 25% chance of coming away with 3x, 3x.
The above concept also applies to the species of the bee, so 25% to come away common common, 50% to be common - forest in either order, and 25% to be forest forest.
Since you're after both common common and 3x 3x, you have a (0.25 * 0.25) 6.25% chance of getting the bee you're after.
Next paragraph is speculation based on real life genetics:
Not entirely sure how the game decides what the active and inactive traits are, I think it works some traits are inheriantly "dominant" and some are "recessive". Dominant traits will attempt to be active unless there is another trait more dominant, while recessive traits will attempt to be inactive unless there is a more recessive trait. Meaning if 3x is recessive, which it seems to be, you'll need a bee with 3x 3x to actually get it to express.
TL;DR get advanced bee machines, it's much easier and not chance based.