(Oxford English Dictionary)
One engaged to eject undesirable or unruly persons from a saloon, ballroom, etc.; a 'chucker-out'. colloq. (orig. U.S.).
1865 Nat. Police Gaz. (U.S.) 29 Apr. 4/2 Old Moyamensing is almost as famous for its lawless gangs of boys and young men, as it was in the days of the 'killers' and 'bouncers'. 1883 Daily News 26 July 4/8 The Bouncer..is merely the English 'chucker out'. When liberty verges on licence and gaiety on wanton delirium, the Bouncer selects the gayest of the gay, andbounces him. 1888 A. C. GUNTER Mr. Potter xx, Several of the fighting brigade of the establishment, that in American slang would be termed 'bouncers'.