I have a system where all the bees are getting pumped from a chest (chest1) to my apiaries. Bees that wont fit ore bees that are being made in the apiaries will then go into another chest(chest2), from that chest(chest2) it gets pumped into my analyzer and then pumped out into chest 1 again so it can be pumped out to all my apiaries.
Once you've manually bred your bee and have stable stackable drones, then you can feed them into an automated loop system, any excess bees can be turned to DNA. If you want to extract the traits, just grab half a stack from the relevant apiary.
Trying to automate mutations with breeding for products is a bit of a mess. I currently use 3 apiaries for manual breeding and analyzing, and 8 apiaries with all the bee species I've found/bred to date.