Have you had any luck researching towns named Bayard?
I can give you info on Bayard, New Mexico and also Fort Bayard, New Mexico both named for George Dashiell Bayard. Fort Bayard came first in 1866. Bayard, the township was named because it was the train station for Fort Bayard in c 1896.
There is an organization in Grant County New Mexico dedicated to preserving the history of the old Fort. It is called the Fort Bayard Historic Preservation Society.