WHEN BOB GOT THROWED, by "Ray" appears in an article "Cowboy Songs and Dances" by Grace B. Ward, in Pearson's Magazine, Vol. 9, No. 1 (Pearson Publishing Company, January, 1903), page 34.

Lyrics are nearly identical to those posted above—the main differences are in the dialect spellings. Then there is verse 2, line 1:

"He crawled on that Andy bronc"

I don't know what an "Andy bronc" is.