1540s, "to disgrace," of uncertain origin. Perhaps a Scottish respelling of bauchle "to disgrace publicly" (especially a perjured knight), which is probably related to French bafouer "to abuse, hoodwink" (16c.), possibly from baf, a natural sound of disgust, like bah (compare German baff machen "to flabbergast"). The original sense is obsolete. The meaning "defeat someone's efforts, frustrate by interposing obstacles or difficulties" is from 1670s. Related: Baffled; baffling.
1839, "to deceive (opponents), especially by betting heavily and with a confident air on a worthless hand to make them 'fold,'" an American English poker term, perhaps from Dutch bluffen "to brag, boast," or verbluffen "to baffle, mislead." The general sense "use a show of confident assurance to deceive an opponent as to one's real resources or strength" is by 1854. Related: Bluffed; bluffing.
An identical word meant "blindfold, hoodwink" in 1670s, but the sense evolution and connection are unclear; OED calls it "one of the numerous cant terms ... which arose between the Restoration and the reign of Queen Anne."