A recording of "Tear It Down, Bed Slats and All," performed by the Memphis Jug Band, appears on "Complete Recorded Works (1932-1934)," Document BDCD-6002, 1990. (There are also numerous recordings of various songs called "Tear It Down," but it's not clear if any of them are what you want.)

Putting "tear it down bed slats and all" (in quotes) into Google yields several references to the song, but I couldn't find any lyrics.