When you get the “bum’s rush,” you’re hustled out the way a bum would be hurried out of a bar or restaurant for begging from the customers.
A bum is a down-and-outer trying to cadge money or drinks. Today, we would probably call him a “street person.” The way it’s done is to grab the bum/hobo/tramp/homeless person by the back of the shirt collar and the back of the belt, and propel him or her out into the snow. Or rain, if it’s the Wet Coast.
“Bum” was first recorded in 1855 and, during the Civil War, was used to describe a foraging soldier. It may have derived from two words: the German bummer, “a high-spirited, irresponsible person,” and the old English word “bum,” which for four hundred years has been slang for both “a drunk” and “buttocks.”
In the 1890-1900s, many saloons had a “free lunch” for customers — sandwiches, pickles, boiled eggs, and so on, to encourage them to stay and buy drinks. Sometimes a penniless man might slip in to the saloon to grab a bite of the “free lunch” without buying drinks. If the bartender spotted him, he’d be rushed out the door and into the street.
In the first part of the 1900s, bailiffs who ejected people from their property, usually in processing a court order to repossess property or enforce eviction, were known as “bums,” and one could imagine that a “bums rush” described a fast and forceful tactic to eject these unfortunates. The upward pull of both the collar and belt caused the malefactor to be light-footed and unable to drag themselves to stop being ejected. Also, this was usually done very fast.
There’s a scene in It’s A Wonderful Life, where Nick, the bartender, says to two other characters, “That’s it. Out you two pixies go — through the door, or out the window.” He gives them the bum’s rush.
I’ve seen the action in various other movies, too. The person being thrown out always very conveniently wore a collared shirt and trousers with a belt. It might not work so well today, if the “bum” is wearing a tee and leotards.