Here's my opinion.

Totally closed population, long-term (think Colonsay). Maybe 30. As each founder queen brings a lot of diversity (including stored as sperm) then a much smaller number of founders would work as long as they were unrelated and as long as you go to a larger population in one step. It is the queen to drone step that really whittles down your genetic diversity.

In a population that can breed to some extent with similar bees in the same region, maybe 6-10. That breeding may be by outcrossing with local drones (assuming that your neighbours also have the same kind of bee, an increasingly rare occurrence) or, in a more isolated situation, by exchange of some stocks on a regular basis.

Of course some progress can be made by beekeepers with fewer stocks, but cooperation regionally is much better.

Another factor is that the more bees you own the greater their dominance of the local drone population. And the greater likelihood that you can breed in the way you wish.

G.