City of Gillette, WY published their municipal code here.
There is no mention of 'bees' or 'hive' in section 4, "Animal and Fowl", nor in section 13, "Nuisances Generally", nor in the Zoning Ordinance. So, no specific prohibition that I could find.
In the Animal and Fowl section, honey bees would fall under the definition of "Animal"
As used in this Code, the following terms mean: (a) "Animal" Any non-human living creature, domestic or wild.
Apparently there are areas zoned in Gillette where you can keep livestock or fowl.
4-3. Livestock. Livestock and fowl may be kept and maintained within the City only in areas which are properly zoned for such use. (C.O. 1948, Ord. No. 773, 3-17-75; Ord. 3769, 8-6-2012.)
There is a provision for "Animal Nuisances" that might be used against someone keeping bees.
4-10. Animal Nuisances. Owners shall exercise the care and control of their animals necessary to prevent them from becoming a public nuisance. Excessive, continuous or untimely animal noise; molesting passersby; chasing motor vehicles or bicycles; attacking other animals; trespassing upon public or private property shall constitute a nuisance. (C.O. 1948, Ord. No. 773, 3-17-75 ; Ord. 3132, 9-18-2000)
Again, they're not specific - but it appears you could be OK to have bees within the city of Gillette.