In 1911, Howard W. Odum printed a number of Oh, Babe, My Babe, Babe verses and songs from southern Negroes. If you are comparing late versions of 'My Babe" and "This Train," you may be right, But both have pre-WW1 antecedents.
See Odum, Howard W., 1911, "Folk-Song and Folk-Poetry as Found in the Secular Songs of the Southern Negroes, The Journal of American Folk-Lore, vol. 24, July-Sept. 1911, no. XCIII, pp. 255 ff.
Some of these; "Baby, What Have I Done," with the lines: Oh me! Oh my! Baby What have I done? Where were you las' Saturday night When I lay sick in my bed? You down town wid some other ole girl, Wasn't here to hold my head.
"Oh MY Babe, Won't You Come Home" paints the reverse picture. Or the man demands freedom, "Where the rounders do as they please, babe!" "Oh, babe, take a one on me," is there. "Things Ain't the Same, Babe, Since I Went Away" "Baby, Won't You Let Me Bring My Clothes Back Home?" 'Well I started to leave and got way down the track, got to thinkin' 'bout my woman, come runnin' back, Oh Babe!' Etc.