I want to know what these expressions mean.
Let's throw the bum out
Throw the bum out attitude
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The literal meaning of bum is a lazy or worthless person. However, in this idiom, it's used metaphorically to refer to members of some group that are not performing up to expectations; it's often used to refer to ineffective politicians, or members of a sports team on a losing streak. Thus, we wish to get rid of those worthless members, and replace them with new ones (who we hope will do better).
If you google the phrase, you'll find lots of web pages referring to the dysfunctional US Congress. It's also used as a rallying cry by some alternative political parties.
There are actually two forms of this traditional American directive: "Throw the bum out!" and "Throw the bums out!" The singular form first appears in the Google Books database in "Isler Astounds Scientists" in The Beacon: Published by the Beacon Staff of Western High School, Detroit, Michigan (1929) [combined snippets]:
The Academy of Science was astounded when Professor Edgar Isler announced that he could and would carry water in a sieve. This caused an uproar, and violent cries were heard.
"Throw the bum out," said Kenneth Wilemon; "toss him on his ear." Professor Isler calmed the irate professors and other half wits . He stated that water could be carried in a sieve and, by chowder, he'd prove it.
But there are two earlier matches for "throw the bums out," from slightly earlier in the 1920s. From The Saturday Evening Post (1926) [combined snippets]:
"Throw these bums out," she commanded—"right out into the street! Trying to force their way into a lady's dressing room!"
"The note——" Ira began.
"Throw the bums out!" Miss Reilly repeated. "It's a trick. I never saw these johns before in my life! Throw them out, Harry—right out on their necks!"
And from Lester Cohen, The Great Bear (1927) [combined snippets]:
Two hours passed. The quarrelsomeness had dropped out of their voices. At intervals, there came a drunken groan, the whine of Vaerring's disabled assertiveness followed by the spattering effusion of his dislike. Then a period of silence, broken by Thane's monotonous growling.
And finally, a deep rumbling, "Henry! Let's throw the bums out." After several minutes, she saw the negro propel one of the men to the door, shove him over the threshold, and repeat the performance with all but Vaerring and Gillis.
As these examples suggest, the original context for the phrase "throw the bum[s] out" was as an instruction to what in the United States is called a bouncer—a rugged employee of a bar, club, or other night spot whose job is to help keep order on the premises and to remove unruly patrons, by force if necessary, when they are no longer welcome.
As Barmar says, the phrase became very popular (in singular form) at sporting events, where the bum in question might be a hapless boxer, an ineffective pitcher, or a player or manager on the opposing team, and (in plural form) in politics, where the bums might be the roster of legislators from an opposing party—or politicians generally.
The meaning remains literally or figuratively the same as it was originally: to eject the unwelcome person or persons from the premises, by bouncer, by umpire, or by ballot.
In the OP's second example, where "throw the bum out" functions as an adjective phrase, the phrase means "having the imperious or peremptory attitude of someone who instructs a bouncer to do his (or rarely, her) work."