Regardless of dictionaries, we have in entomology a rule for insect common names that can be followed. It says: If the insect is what the name implies, write the two words separately; otherwise run them together. Thus we have such names as house fly, blow fly, and robber fly contrasted with dragonfly, caddicefly, and butterfly, because the latter are not flies, just as an aphislion is not a lion and a silverfish is not a fish. The honey bee is an insect and is preeminently a bee; “honeybee” is equivalent to “Johnsmith.”

—From Anatomy of the Honey Bee by Robert E. Snodgrass

The non-native European Honey Bee is the state insect of:

Arkansas
Georgia
Kansas
Louisiana
Maine
Mississippi
Missouri
Nebraska
New Jersey
North Carolina
Oklahoma
South Dakota
Tennessee
Utah
Vermont
West Virginia
Wisconsin

Not one native bee is a state insect. The closest relative of a North American native bee to make the list is the Tarantula Hawk Wasp, the state insect of New Mexico.

Update! Minnesota now has a state bee as well as a state insect. Bombus affinis, the Rusty-Patched Bumble Bee, has been so honored. Good work, Minnesota!