The conventional view is that the "escape" of varroa from it's original habitation region was caused purely by migratory beekeeping starting at about 1900. I admit that this seems to fit the later distribution and spread quite well. I believe that there is another subtle mechanism at work within the time scale of 1890 to the present day.
My view is that varroa and bees have both existed side by side for a period of millions of years and that during this time there would have been many challenges of varroa to our Apis mellifera strains of bee. It is not until 1900 or so that this becomes noticed "as a problem" and even then at a low level until around 1950 when the pace of spread accelerated.
This time scale corresponds with the initial introduction of beeswax foundation into beekeeping. This foundation was initially made the same size as the bees would make for themselves, but by a series of accidental and deliberate steps this original sizing has gradually been increased so that it is now at least 10% and in some cases as much as 20% too large. See "640" Cell Size Bees.
The bees have kept pace with these incremental increases in cell size by increasing their own physical size. Some of the deliberate cell size increases were done for this exact purpose. I believe that this larger "bloated" bee is less fit in several ways and is thus less able to withstand the onslaught of varroa.
My suggestion is that a challenge occurred at about 1900 (that may well have been due to migratory beekeeping) and that the bees were less able than they had been previously, to withstand the varroa mites and thus varroa established a "bridgehead" and has been associated with apis mellifera ever since.
As most authorities are "absolutely certain" of the accuracy of the conventional view there has been little need to look further or in greater detail at the evidence.
The tenacity with which the conventional view is held results in few items of reference that can be quoted for a possible alternative. However I list the following from Apimondia 1979, in the hope that others may consider the plausibility of my case.
 page 56, Dr Marin pointed out that the disease has spread over a larger area with the increased queen imports and more extensive migratory beekeeping. But the former have been practiced for a long time, and the latter for centuries.
 My comment: The fist major wave of cellsize increases took place around 1900 and a second wave took place around the first half of the 1930's the disruption of WWII may well have caused the delay before the accelerated spread was noticed around 1950. (This is disputed by some.)