Justa Picker's playing (not a clip!; "Bye Bye Bluebell/Old Joe Clark - Medley" (1:58)) is HERE. Probably Doc learned this from Merle Travis' "Goodbye My Bluebell". The original sheet music is (from Levy: CLICK HERE):

Title: Blue Bell. March Song & Chorus.
Composer, Lyricist, Arranger: Words by Edward Madden. Music by Theodore F. Morse.
Publication: New York: F.B. Haviland Publishing Company, 1904.
Form of Composition: strophic with chorus
Instrumentation: piano and voice
First Line: Blue Bell, the dawn is waking, Sweetheart you must not sigh
First Line of Chorus: Good-bye my blue Bell, Farewell to you
Performer: [Edward B. Adams]

~Masato