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Fans line up for the first taping of "The Late Show With Stephen Colbert" on Sept. 8. Credit Michael Loccisano/Getty Images

During the taping of his first show as host of “The Late Show” on CBS, while interviewing Jeb Bush, Stephen Colbert explained how he, the real Stephen Colbert, was different from the character he had played for nearly 10 years on “The Colbert Report.”

“I used to play a narcissistic conservative pundit,” Mr. Colbert told Mr. Bush and his studio audience on Tuesday night. “Now I’m just a narcissist.”

That persona may be retired, but in this first episode of “The Late Show With Stephen Colbert,” the arch and up-to-the-moment sense of humor that Mr. Colbert cultivated on his Comedy Central political satire series was still very much in evidence when he made his debut on Tuesday as host of a network late-night talk show.

(This episode was recorded in a two-hour taping at the Ed Sullivan Theater in Manhattan.)

The show began with a mostly sincere pretaped segment in which Mr. Colbert and other musicians performed “The Star-Spangled Banner” in various locations around New York and the United States (including a bowling alley and the Fort Worth Stockyards in Texas).

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Jeb Bush, left, on “The Late Show With Stephen Colbert.” Credit Jeffrey R. Staab/CBS

After taking the stage to enthusiastic applause, Mr. Colbert opened with a stand-up monologue in which he observed, “If I knew you were going to do that, I’d have come out months ago.”

After an opening credits sequence, Mr. Colbert sat behind his desk and continued to perform a set of topical jokes, using TV-news-style graphics that would not have been out of place on “The Colbert Report.”

Not surprisingly, many of these jokes were about Donald J. Trump, the outspoken leader in polls for the 2016 Republican presidential nomination. Noting that Mr. Trump has been favorably received by white supremacists, Mr. Colbert said this was “amazing” because “Trump’s not even white — he’s more Oompa-Loompa American.”

While interviewing Mr. Bush, the former governor of Florida (and brother of President George W. Bush, the subject of a merciless roast that Mr. Colbert performed at the 2006 White House Correspondents’ Association dinner), Mr. Colbert asked him straightforward policy questions about education and gun control.

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George Clooney was the first guest on Stephen Colbert’s inaugural “Late Show” on Tuesday.

But there were also many humorous flourishes. Mr. Colbert teasingly asked Mr. Bush about his use of an exclamation point in his campaign poster (“It connotes excitement,” Mr. Bush explained) and referred to remarks by his mother, Barbara, in which she said the country has “had enough Bushes” in the White House (“She was just joking,” Mr. Bush said).

Mr. Colbert also offered him new talking points to use in presidential debates that the host said sounded “Trumpier.” Among these upgraded lines that he had Mr. Bush recite were “I will build a wall between the United States and Iran.”

Earlier in the program, Mr. Colbert conducted an interview with George Clooney in which he gave the actor a belated wedding gift to congratulate him on his 2014 marriage to his wife, Amal, a human-rights lawyer. Mr. Clooney opened a box from Tiffany & Company to find a paperweight with the inscription “I don’t know you.”

The taping occasionally had to be halted so segments could be rerecorded to correct for technical glitches. (Before Mr. Bush taped his stage exit for a second time, Mr. Colbert told the studio audience, “Sit down and get ready to fake another orgasm.”)

Even the show’s concluding musical number, an all-star performance of “Everyday People” featuring the soul singer Mavis Staples and Mr. Colbert’s bandleader, Jon Batiste, had to be recorded twice.

Mr. Colbert seemed to take it all in stride. Before the unexpected encore, he said with deep sarcasm, “It’s not like anybody put any effort into it the first time.”

Correction: September 8, 2015
Because of an editing error, an earlier version of this article included an erroneous reference to the number of minutes longer than normal that Stephen Colbert’s “Late Show” debut was scheduled to run. It was 7 minutes, not 12.