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.