"(Olban,) The White Captive," was collected by Phillips Barry in Maine (DT); Barry and the Traditional Ballads Index credit the song to Thomas C. Upham, 1818 (later a professor at Bowdoin College), 'The Columbia Sentinel,' Boston; Barry gives some details in "The New Green Mountain Songster," Flanders et al., pp. 256-258 with score, but full details were printed by Flanders et al. in FSSNE Bull. No. 8, pp. 19-24.

The song was collected in North Dakota in shortened form (G. F. Will, Songs of Western Cowboys, JAFL, vol. 22, no. 84, 1909). The cowboy who sang it said he first heard it on a South Dakota Ranch, from a Texas cowboy, who said he had learned it in Mexico from another Texas cowboy, who sang it to the cattle when on night-guard.
Randolph collected versions from the Ozarks and Colorado under the title "Her White Bosom Bare." This image in the song undoubtedly contributed to its wide spread and numerous versions.

The tune in the score given in Flanders et. al. for "The White Captive" is quite different from the midi at Mudcat and the score in the Digital Mirror- http://sniff.numachi.com/~rickheit/dtrad/pages/tiWHTCAPTV;ttWHTCAPTV.html
The melody of the score in Flanders et al. was written down by Mrs. Grace Fisk Bartlett, Cabot, Vermont, and printed in the FSSNE, Bull. No. 8, p. 23. A note says that the first part of the fourth line of each verse must be repeated to conform to the tune.

It would be interesting to trace the song from its first printing in the Boston Columbian Sentinel; it must have been reprinted in other papers or sheet music in order for it to have spread so widely.