You noted you were not related to the Bybee Family.
However, just FYI, here the Bybee names of Rigby, Idaho.
Infomation extracted from "The Hub of Eastern Idaho" by Patricia Lynn Scott
Afton Bybee - No information
F.M. Bybee - Of Menen. Snake River Valley Telephone Co. incorporated July 1897. F.M. Bybee became Secretary at that time.
Lawrence Bybee - Manager, Rigby Flour Mill.
October 4, 1923: Rigby Flour Mill - Bybee was repairing machinery when it caught on fire and destroyed the Mill. Bybee was pulled from the fire by E.E. Rapp and was saved.
Mary L. Bybee - Wife of Owen Sayer. Married 1873, Uinta, Utah.
Walter A. Bybee - County Commissioner 1st district 1909-1910