Are you sure any lyrics exist? I've been unable to uncover any evidence of lyrics. Most ragtime tunes, such as those by Scott Joplin, don't have lyrics.

However, there are a couple of books that might contain some useful information:

Blind Boone: Missouri's Ragtime Pioneer by Jack A. Batterson (Columbia: University of Missouri Press, 1984).

Kansas City Jazz: From Ragtime to Bebop—A History by Frank Driggs, Chuck Haddix (New York & Oxford: Oxford University Press, 2006.)
It has a chapter titled "Carrie's Gone to Kansas City" and lots of information about the composer, John William "Blind" Boone.

Only parts of those book can be "previewed" at Google Books.