> Revising my question - how might selection on honey bees result in the reduction of mite fertility? 

As early as 1999 and probably before, researchers identified traits in bees that affected mite reproduction. Harbo & Harris write:

There are presently many mechanisms
of resistance that show promise. We think
that the suppression of mite reproduction,
hygienic behavior and proportion of mites in
brood (the tendency for adult mites to not
enter brood cells) are presently the three
most promising of the specific characteristics
that are heritable and should respond to selection.

Because non-reproduction of mites
was found to be a heritable characteristic of
bees (27], we call it suppression of mite
reproduction. This characteristic has been 
linked to resistance to V. jacobsoni by many investigators

John R. Harbo*, Jeffrey W. Harris. Selecting honey bees for resistance to Va"oa jacobsoni. Apidologie 30 (1999) 183-196

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