Phoresy is a noun that describes a nonparasitic relationship whereby one species is carried about by another. The relationship is usually commensalistic, meaning one organism benefits from the association but the other organism is unharmed by it. Phoretic is the adjective.
Varroa mites that can be seen riding on adult honey bees are often referred to as phoretic. But if the word “phoretic” implies a non-parasitic relationship, then I believe the term is used incorrectly. Free-loading Varroa mites are known to be eating as they ride—much like passengers on a dinner train—except they are sucking fluids from their host. If the Varroa mites are actually consuming hemolymph as they are transported, I would argue their relationship is a parasitic one—a relationship not contemplated by the term “phoresy.”