As with many slang words, the etymology of boogie-woogie is difficult, if not impossible to trace. There is a Bantu word, mbuki-mvuki, that may very well be the linguistic ancestor of boogie-woogie.
Mbuki-mvuki means to take all one's clothes off in order to better be able to dance. Now doesn't that sound just like boogie-woogie?
Source: Rheingold, Howard, They Have a Word for It, 1988, Jeffrey Tarcher Inc, Los Angeles.