Entries linking to hub-bub
"confusedly, hurriedly," 1590s, a "vocal gesture" [OED] probably formed from pig and the animal's suggestions of mess and disorder. Reduplications in the h-/p- pattern are common (as in hanky-panky, hocus-pocus, hinch(y)-pinch(y), an obsolete children's game, attested from c. 1600).
Edward Moor, "Suffolk Words and Phrases" (London, 1823), quotes a list of "conceited rhyming words or reduplications" from the 1768 edition of John Ray's "Collection of English Words Not Generally Used," all said to "signify any confusion or mixture;" the list has higgledy-piggledy, hurly-burly, hodge-podge, mingle-mangle, arsy-versy, kim-kam, hub-bub, crawly-mauly, and hab-nab. "To which he might have added," Moor writes, crincum-crankum, crinkle-crankle, flim-flam, fiddle-faddle, gibble-gabble, harum-scarum, helter-skelter, hiccup-suickup, hocus-pocus, hotch-potch, hugger-mugger, humdrum, hum-strum, hurry-scurry, jibber-jabber, prittle-prattle, shilly-shally, tittle-tattle, and topsy-turvy. Many of these date to the 16th century.