The mathematics of genes
A complex behavioral trait, like VSH, is the expression of dozens of genes. It is not a single gene turned on and off. The expression likely requires "homozygous recessive" or "rr" in at least some of these genes (as the trait appears infrequently in the wild).
For example, let's say VSH is linked to 10 genes. Mendelian ratios say the expression of VSH will be seen 1/4*1/4....*1/4 of the time or 1 in 4^10 (4 to the 10th power) -- that is 1 in 1,048,576 colonies will have the proper gene expression. Strictly mathematically, only about 3 of all kept colonies in the US would have the right expression (using the arbitrary 10 homozygous genes as the assumption).
Inbreeding the one-in-a-million colony, could fix the trait, so daughter clones would express the VSH. Moved out to the wild, only 1 in 2^10 (or 1024) one-in-a-thousand colonies would have the trait in the F1 (second generation) if the dominant and recessive genes were equally present in the wild population of drones.
A complication of bee biology is the wild mating with multiple drones, VSH would need to be frequent enough among the multiple fathers to make a difference in the hive biology and survival.
Unfortunately, inbreeding to fix a trait has the deleterious effect of fixing a lot of sub-lethal bad things in the geneotype. Think Appalachia Cousin Marriage yielding six-toed cretins. This "inbreeding depression" is compensated for by controlled out-breeding, and reselection of the desirable expression. -- This is why traditional breeding programs are multi-decade efforts.
Remember that orchard crops are grafted clones, this is because the F1 of these trees in an even inbred cross are a mish-mash (or back to the one-in-a-million lottery expression of taste and color). I don't know if grafted clones of bees are possible in a lab setting (drones are haploid or 1/2 of the queen's genes, so would be a resorted mix of her pairs of chromosomes).
The F1- one-in-a-million- lottery and the inbreeding depression cost is controlled in plant breeding by hybrid selection. In hybrids, specialized parent strains that are infertile are maintained. The mother cannot produce (pollen) and the father won't set seed. Mothers can be chemically, manually, or in some cases genetically sterilized from producing pollen (aka Drones in a bee metaphor). The father/pollen/drone strain is a separate genotype that adds back just enough other traits to compensate for the weaknesses of the mother genotype. In plants, many hybrids are F2, parents are used to produce F1, which are then crossed to a second generation with the proper combination of traits. I realistically don't see how a hybrid selection model would work for bees as the selection and maintenance of non-productive parent colonies seems out of reach practically.
