Around here honeybees do not compete with wild bees for much. Honeybees are a domesticated non-native species incapable of pollinating most native plants. Native bees are well adapted to pollinating native plants but have trouble with the non-native plants.
The problems that native bees here have are several.
o Insecticides (aka pesticides) applied to agricultural crops affect all insects, good and bad, including bees.
o Loss of, for lack of a better word, habitat. Native species of plants are displaced by introduced species that the native bees can not harvest nectar from. Note that urbanization isn't really a big problem for bees because there are plenty of flowers in the city. But are they the right kind of flowers? Orchards full of foreign plants like tree nuts on the other hand, is loss of habitat.
o Introduced disease. Not only are foreign bees brought in (eg. honeybees) but foreign honey is brought in from far away continents chalk full of spores of varieties of nosema or foulbrood or other threats. Honeybees catch these diseases, and bring varroa and tracheal mites and other problems, and spread them to the native bees.
o Honeybees are domesticated agricultural animals like beef cattle and pigs. If the numbers decrease we just breed more until market demand is met. It takes 21 days to breed a new queen and split a colony. Native bees, well, they rely on natural methods of reproduction. The birds and the bees, literally.
As to how a big colony of honeybees deals with a virus: they don't just "throw out the infected bees" since it usually affects the brood more than the workers. If the brood dies, there will be no more workers in a few weeks and the colony collapses. How it usually gets dealt with is the beekeeper medicates the hive. Or, in the case of foulbrood, digs a pit, burns the hive and all nearby hives and all equipment, and buries it like so much nuclear waste.
There is no threat to honeybees. No such luck for wild bees.