One explanation is that it's a corruption of "the business". Another is that it should be "Bs and Es", an abbreviation for "be-alls and end-alls".
But apparently the most likely is that it's just one of a set of nonsense catchphrases from the 20s: flapper-speak. Others included "cat's miaow", "elephant's adenoids", "tiger's spots", "bullfrog's beard", "elephant's instep", "caterpillar's kimono", "turtle's neck", "duck's quack", "gnat's elbows", "monkey's eyebrows", "oyster's earrings", "snake's hips", "kipper's knickers", "elephant's manicure", "clam's garter", "eel's ankle", "leopard's stripes", "tadpole's teddies", "sardine's whiskers", "pig's wings", "bullfrog's beard", "canary's tusks", "cuckoo's chin" and "butterfly's book".
Take your pick!