Bees? Egads, do I have bees. I'll pass along some of my tips on improving bees; with an example.
First, my usual setup. Four apiaries in a row, all containing pure versions of the starting bee; I normally keep four hives for each bee species unless I'm trying to collect a specific resource (like silk). For my purposes, a pure bee has the same trait on both sides for every category.
You set this up by putting a starting pair in the first apiary, to the left or right (just keep doing it the same way, I go from left to right) and whatever princesses you have in the other three (usually meadows or forest). Keep breeding the first princess/drone combo and the others with nothing but drones from that first hive. After a few generations, check the princesses in those other hives with a beealyzer. When a princess matches the first one exactly, put it in the 2nd hive and a drone from the first; after that those bees are clones of the first and will always remain so. I put a sign on the rightmost hive of a group of clones (with Lifespan, Speed and Drones) so I don't have to check to see what any bee behind or to the left of that sign is.
Repeat with drones from hives 1 and 2 until you get a third, move the sign, put one of the drones from 1 or 2 in with the third in apiary 3 and you now have 3 sets of clones, the fourth quickly follows. After I get four I can start breeding/improving them. I always breed the last 3 and keep the first pure in case things go badly wrong, in which case I can just repeat this section and reset all four bees to where I started.
As an example, I'll just focus on one trait; lifespan. Let's say I have a Noble/Short and a Valiant/Long and I want to breed Noble/Long. For this example, all the other traits are identical and they have x2 drones. When you first cross them, the princess picks one of the two traits from her traits, since both are Short, you end up with Short, one of the two traits for the drone is always Long. The same with species, the Princess side always picks Noble, the Drone side always picks Valiant.
So the 3 princess and all 6 drones will have Long/Short for lifespan and Noble-Valiant for species (for breeding purposes Noble/Valiant and Valiant/Noble are identical). This is what happens every time you breed two pure bees together. For the first crossing, you know what every bee is, so there is no need to identify them and waste valuable honey. So you cross them, trust to luck and here is what you could get (traits picked at random).
3 Princesses (Best to Worst) Noble - Short/Long, Noble-Valiant - Short/Long, Valiant - Long/Long
Drones (Best to Worst): Discarding any Short/Short out of hand (as we have all the pure Noble - Short/Short we want in Hive #1) we end up with Noble - Long/Short, 2x Noble-Valiant - Long/Short, Valiant - Long/Long, 2 x Valiant - Long Short. I usually keep the extra drones from the first crossing to guard against bad luck, so in this case I'd also have 3 Drones Noble-Valiant - Long/Short if I got too many Valiant pure bred drones.
Our best bet so far is the Noble Long/Short Princess and Noble Long/Short Drone, but we also match up the 2nd and 3rd bests and mix them as well. Picking traits at random again we get:
Princesses: 2x Noble-Valiant Short/Long, Noble - Short/Short (not much better)
Drones: Noble - Long/Long, Noble - Long/Short, Noble-Valiant - Long/Long (getting better), ignoring pure Valiants and Short/Short.
Mixing again (random picks after crossing the best princess with the best drone, 2nd with 2nd, ect.)
Princesses: Noble - Long/Long, Noble - Long/Short, Noble-Valiant - Long/Short
Drones: 3 best are all Noble - Long/Short
At this point what we are looking for is a Noble - Long/Long Princess and Noble - Long/Long Drone. When we get those we can put them into Hive #1 and turn any bees we want into Noble/Long bees. With this many traits out of the six bees being Noble and Long, it should only take about 2-4 more generations to get the bees we need.
One of the keys to my success is more drones, they are like lottery tickets and the more you buy the better your chances are. Once you breed a x4 Species and make it pure, take the time to go back and make all your existing species x4. This will make creating new species and improving your lines a lot easier since you will have twice as many "tickets" in the genetic lottery you're playing trying to find the best drones for your princesses.
Keep in mind that you don't have to breed a pair if you don't want to, if you only get two good drones out of the bunch; just breed those two with your best princesses and hope for three good ones next time.