In an interview, Mr. Bloomberg said he did not believe that voters would see this as an election where charisma is paramount, given how deeply many Americans feel that President Trump has led the country in the wrong direction.

As president, he said, “You have to have somebody that the public thinks, ‘Whether I like the guy or the woman or not, he is smart, well meaning and knows how to manage the process.’” As for the subject of his wealth, he said, “it’s tricky,” adding: “People in America fundamentally don’t want to take away what you have. They want to find a way so that they can get it as well.”

So his speeches include a line that hits directly at the self-made part of his biography, and a personal critique of the president’s signature legislative achievement, the 2017 tax cut, in which the benefits went disproportionately to wealthy people like Mr. Bloomberg.

“I didn’t need a tax cut, thank you very much,” he said last week in Oklahoma City.

Still, delivering a good line off a teleprompter — Mr. Bloomberg reads from one at almost every public event — means little if he cannot nail the moments when the script isn’t there. And then there are the times he mangles the script anyway, like telling the crowd in Greensboro, N.C, how nice it was to be in “Gainesboro.” Or how much he was looking forward to competing in “Super Bowl Tuesday.”

His audiences seem not to mind terribly much. In Greensboro, a few people in the crowd called out to correct him, but that was the end of it. “Very, very impressed,” said Jimmy Sipsis, 60, a property manager and self-described independent. “Based on his record, you look at it, and see he can stand up there and say, ‘I’ve done this, I’ve done that.’”

Once Mr. Bloomberg entered the race late last year, the campaign benefited from almost two months in which the candidate could hone his public speaking skills, rusty and sclerotic after a decade since his last run, without too much scrutiny. The attention of the political world was trained on Iowa and New Hampshire where Mr. Bloomberg did not compete, so hardly anyone noticed the gaffes like when he opened a campaign office in Denver in early February and joked about wishing someone else could have spoken for him so that he could spend the day at his home in Vail, Colo.