Black Bottom refers to a dance which became popular in the 1920s, during the period known as the Flapper era.
The dance originated in New Orleans in the 1900s. The theatrical show Dinah brought the Black Bottom dance to New York in 1924, and the George White's Scandals featured it at the Apollo Theater in Harlem 1926 through 1927. Jelly Roll Morton, jazz player and composer, wrote the tune "Black Bottom Stomp" with its name referring to Detroit’s Black Bottom area. The dance became a sensation and ended up overtaking the popularity of the Charleston, eventually becoming the number one social dance.
"Ma Rainey's Black Bottom" is a song by Ma Rainey which makes obvious allusions rather than being dance music.