A “buck nun” is an old West term (cowboy slang) for a bachelor. One source below states that a “stud horse” is an opposite term.
     
   
(Dictionary of American Regional English)
buck nun n [buck n 2] chiefly West
A celibate man; a man who lives alone.
1907 White AZ Nights 286, I might as well go be a buck nun and be done with it.
1944 Adams

, Buck-nun—A recluse, a man who lives alone.
1961 Adams Old-Time Cowhand 202, Men selected to winter in them camps were usually single men with few or no home ties, and didn’t mind the life of a buck nun. Ibid 342, You take some old buck-nun who’d never been hogtied with matrimonial ropes, and he didn’t savvy she-stuff.
1967 Cerello Dakota Co MN 47, Buck nun...A priest or other celibate clergyman—“I always felt sorry for the poor sisters that taught us, but those buck nuns really had the life…they owned cars, could come and go as they pleased, had money…” [Heard in] 6 communities.
 
(Historical Dictionary of American Slang)
buck nun n. West, a reclusive bachelor. Joc.
1907 S.E. White, Ariz. Nights ch. iii: I might as well go be a buck nun and be done with it.
1944 R. Adams West. Words 22: Buck-nun—A recluse, a man who lives alone.
1967 in DARE I 420.
 
Google Books
Arizona Nights
by Stewart Edward White
New York, NY: The McClure Company
1907
Pg. 286:
“I might as well go be a buck nun and be done with it.”
   
Roundup Recipes
by Bonnie & Ed Peplow
with the help of the Arizona Cowbelles
Cleveland, OH: The World Publishing Company
1951
Pg. 263 (Glossary):
BUCK NUN: A bachelor.
 
Google Books
Arizona Quarterly (1954?)
Pg. 39:
The cowboy faced the business of courting, marriage, and raising a family with mixed emotions, but with a rather orthodox set of morals. A buck nun was a virtuous bachelor, whereas a stud horse was a virile bachelor with few moral compunctions.
 
Google Books
Dictionary of the American West:
Over 5,000 terms and expressions from Aarigaa! to Zopilote
by Win Blevins
Seattle, WA: Sasquatch Books
2001
Pg. 48:
BUCK NUN A hermit; a cloistered male.