How to identify the subspecies/breed of a bee
I am not sure about apiculture, but in academic research it is typical that people use microsatellite markers for identifying subspecies of bees. Microsatellite are repetitive regions of the genome that are useful in at identifying different species/subspecies, as well as for generating pedigrees and paternity analysis. Different species/subspecies have different numbers of repeats in a particular microsatellites, and these differing number of repeats are heritable. People use microsatellites because they are cheap, easy to run and reliable for identifying species/subspecies. Because there can be many different alleles (or different numbers of repeats) at a given microsatellite locus, so you only need relatively few microsatellites in total to identify individuals.
An example can be found in this paper. They used 7 microsatellite loci and could reliably identify between different African and European sub-species. It is worth a read of the intro:

Recent population genetic surveys in human (Bow- COCK et al.
1994;DIRIENZO et al. 1994) and other mammals (GOTTELLE et al. 1994;
TAEOR et al. 1994) and in bumble bees (A. ESTOUP,M. SOLIGNAJC. ,M.
CORNUET and A. SCHOLL unpublished results) have shown that
microsatellites are highly efficient at differentiating
populations or groups of populations. In this paper, we investigate their
usefulness for honey bee population studies by adressing the
following specific questions: Are the three evolutionary branches
inferred from morphometry and mtDNA confirmed by microsatellite
data? Are microsatellites useful for differentiating sub-species and
populations within subspecies? How does the pattern of variability of
these markers vary between branches/subspecies/populations and which
factors may be invoked to explain it? Is it possible to assign a given
colony to its population of origin from microsatellite data and how do
the individuals from this colony cluster within the population?

References:
Estoup A, Garnery L, Solignac M, Cornuet JM. Microsatellite variation in honey bee (Apis mellifera L.) populations: hierarchical genetic structure and test of the infinite allele and stepwise mutation models. Genetics. 1995 Jun;140(2):679-95. PMID: 7498746; PMCID: PMC1206644.