There are as many tunes for this as a cat has whiskers. These are given, with the texts, in the book by Fife and Fife entitled "Songs of the Cowboys," N. Howard (Jack) Thorp, Variants, Commentary, Notes and Lexicon."

XI-B; The Cowboy's Hat, or The Bucking Broncho (Dobie, More Ballads). P. 125.

XI-G: My Lover's a Rider (Hull, in Kansas State Hist. Soc.) pp. 56-57.

XI-H: "My Love Is a Rider (Larkin, in Oak) pp. 46-47

XI-L: "Bucking Bronco (FAC I 509 sung by Kathy Degel, Kansas.

Texts without tunes-
Thorp, Lomax, James Hatch from Dobie, Lomax d. 5620, Hobo News, Watson (WPA, NM).

The Fife's comment, "There are several melodies... although common elements prevail. The music typically reveals tendencies that support the texts they accompany. ... there is a frequent and persistent return on the strong beats of the measure to the same note. Such a melodic structure could easily suggest the rhythmic, stiff-legged bucking of a bronco.
"Dobie's tune (Text B) is very significant, though not conforming to the statement above. Also important are the Hull ((Text G ) and Larkin (Text H) texts, the latter being the best setting of the most usual melody."

Lists of Commercial and Field Recordings, pp. 133-134.