Yes, OP, you are correct. Injecting into one but not the other means you've left it up to random luck, and eventually the trait will disappear completely. Usually sooner rather than later.
I make a "Super Bee" (can be any species, it doesn't matter) which has all the best traits injected into it. I make one princess and one drone, cycle them thru an apiary to make stacks of drones, then use the stacks of drones to convert random pristine princesses into more Super Bees.
When I breed a new species, I extract it and inject it into a "Super Bee" pair and use these two bees to make stacks of the new species because it reduces the waiting time.
When I acquire a new and improved trait, I change my "Super Bee" to the new version, breed em up, and throw the old Super Bees (which now obv aren't quite so super) into the DNA grinder thing.
The hardest part of bees is going from Meadows/Forest thru Imperial/Industrious because that's all done manually except for the helpful assistance of apiarist pipes and autarchic gates. One you've got royal jelly and pollen going, alveary production begins and you just roll downhill from there. I'm going thru the manual process myself right now in my Monster SSP world. Tedious, but bees are well worth the time and efforts.