Roberts in 1944 recorded 1 to 4 flights. Queens must orient to their hive like other bees, and need test flights to learn the landmarks, but have active mating on 1 or more flights.
Read the article "Causes of Repeated Mating Flights" available for download at: http://jerzy_woyke.users.sggw.pl/causesmat1964.pdf
Honey Bee mating is *obligate* out-crossing. Inbred mating with related drones cause shot-brood (50% of the larvae are lethal) and unusual diploid drones (that are also lethal). There are multiple sex alleles to ensure outcrossing -- a Julian Adams paper measure 19. The outcrossing alleles are unfamiliar to mammal genetics, but these obligate mechanisms are common in plants, etc. Read the Julian Adams paper-- http://www.genetics.org/content/86/3/583.full.pdf
A local population of 10 hives with freely mating queens *may* have enough variation to avoid inbreeding issues. The brood pattern will show you. If there are shot-holes (failed larvae) then the genetics have gone bad, and you need to import new stock to increase out-breeding.
A paper on observations in Germany reports 1-3 mating flights in their queens SEE: http://www.researchgate.net/publication/220022996_Multiple_nuptial_flights_sperm_transfer_and_the_evolution_of_extreme_polyandry_in_honeybee_queens/file/9fcfd50c7a48fbaaaf.pdf
This paper also reports 14% of the queens failed to return after the flight. This is similar to my (unquantified) experience on loss of queens from walk-away splits.
A more recent paper (not yet available without cost) is:
No Behavioral Control over Mating Frequency in Queen Honey Bees (Apis mellifera L.): Implications for the Evolution of Extreme Polyandry.
David R. Tarpy and Robert E. Page, Jr.
The American Naturalist
Vol. 155, No. 6 (June 2000), pp. 820-827
((contact me if you want to review).