Thanks for reaching out with this question. I'm not aware of birds being a major predator of honey bees in Michigan. In my beekeeping experience, even if some birds eat adult honey bee workers, they do not cause noticeable damage to a colony.

I'm not an expert in birds, but here is what I was able to find about Eastern Bluebird and Barn Swallow diets:

Managing Habitat for Eastern Bluebirds (psu.edu): "Insects, including grasshoppers, crickets, beetles, and caterpillars, make up 68 percent of a bluebird's diet, while the remaining 32 percent is fruit."

The Eastern Bluebird (umd.edu): "Throughout the breeding season, mating pairs can be seen bringing the nestlings crickets, grasshoppers, beetles, and moth larvae."

Barn Swallow (umd.edu): "In addition to flies, Barn Swallows consume beetles, leafhoppers, wasps, ants, moths, grasshoppers, and crickets."