exclamation of contempt, 1817, probably from French bah, Old French ba, expressing surprise, scorn, dismay. Perhaps simply a natural exclamation in such situations; compare Greek babai!, an exclamation of surprise. De Quincey condemned it as a coarse French import.
Twenty five years ago the vile ejaculation "Bah!" was utterly unknown to the English public. Now, and entirely through the currency given to it by our own novels, it has become the most popular expression for dismissing with contempt any opinion or suggestion of the person with whom you are conversing. Sir Edward Lytton was amongst the earliest and deepest offenders. ["French and English Manners," 1850]