The popularity of the Pickard Family version (American Record Co. master)is attested to by its many releases:
Perfect12625, Banner 0744, Conquerer 7574, Oriole 1995, Challange 882, Jewel 5995, Pathé 32546, Perfect 12625, Regal 10049, Cameo 0344, Domino 4845, Romeo 1357, Paramount 3218, Broadway 1850 (Norm Cohen, "Long Steel Rail").
No wonder their lyrics are remembered.

The lyrics in Vance Randolph, Ozark Folksongs, Song 511, vol. 3, pp. 277-278, add little to what appears here and in the DT.
Mrs. Maggie Morgan, Springdale, Arkansas, 1942 ("heard the song in the 90's").
Riding on the Dummy

Of all the ways of traveling, by coach or carryall,
By steamer, stage or railway car, the dummy beats them all;--

What follows is the same as the text of the Booth-Carnes song of 1885, posted by Joe Offer.

Randolph says this version was printed in the "Merchant's Gargling Oil Songster, Lockport, NY, 1887, p. 32, "By permission of George W. Hagans... San Francisco, CA, who will furnish words and music for 25 cents, sample copy."
He then remarks that the front part of streetcars used in California in the early days was open and was called the dummy.