To bounce is to eject summarily.
1882. Gibson Bounced. A Blackmailer kicked out.—Heading in Washington Republican, Jan. 28.
1884. Speaker Carlisle has bounced his clerk for telling tales out of school.—Boston Journal, Oct. 3. (N.E.D.)
1888. The [land] jumpers did not go, whereupon the Mayor ordered his force to bounce them, and tear down their shanties, &c.—Cincinnati Gazette, Feb. 22 (Farmer).
1890. The widow of a miner, who kept boarders, was also on the scant list of female acquaintances of one of the frontiersmen, who describes a person called the “bouncer,” who seems to be a well-recognized functionary is such establishments. He is always big and strong, and his duties consist in bringing to time people who neglect to pay their bill, and for this service he is boarded without charge. An Eastern man, a “tenderfoot,” on one occasion asked some one to pass the gravy, whereupon the bouncer placed his pistol on the table and quietly remarked, “Any man as calls sop gravy has got to eat dust or ’pologize.”—Mrs. Custer, ‘Following the Guidon,’ p. 31 (N.Y.).
