Jeb Bush’s nascent presidential campaign has already won over many of the big-dollar donors and GOP elites. What he needs to prove now is that he can win over the crowds.

Until visits to South Carolina and other early states this month, the former Florida governor hadn’t been on the campaign trail for himself in 13 years. He hadn’t sold himself to the deeply conservative, tea party-inspired crowds that have emerged as a driving Republican force in the Obama era. He’d never snapped so many “selfies” with admirers.

And he admits his delivery is a work in progress. “I’m learning along the way how to get better,” he told reporters in South Carolina this week.

And what has he learned? “I think if you’re on a long journey and you start at X, if you have any kind of aspirational nature in who you are, you’re expecting to get to 2X, 3X, 4X,” he said. “I’m goal-driven, and I can assure you I’ll get better at whatever it is I need to do.”

The exchange sums Bush up well. One moment he’s lofty; the next he’s granular. There are fleeting moments of personal connection, but mostly he’s proudly workmanlike — and unafraid to come off as the smartest guy in the room. He has a Bill Clinton-like ability to speak on multiple issues with fluency, but with a mechanical delivery in place of a friendly drawl.

Bush is casting himself as the experienced adult in a Republican field packed with younger, crowd-pleasing contenders, from Gov. Scott Walker of Wisconsin to Sen. Ted Cruz of Texas. The question is whether his wonky, somewhat stilted approach will have appeal beyond the ranks of the establishment GOP.

“Clearly, he’s smart, there’s no question about that,” said Bob Knight, a lobbyist who watched Bush speak in Greenville and ­Columbia, S.C. “You can buy that — but can you buy charisma? Does he have the charisma to win?”

Bush starts his standard stump speech with a quick nod to his family history. In Cedar Rapids, Iowa, he introduced himself as “George’s boy and W.’s brother,” but quickly put distance between himself and the former presidents.

“All of my mistakes I made in my life are my own doing. They have nothing to do with my family. I have a great family. But I’ve been on my own journey,” he said.

When he made his first stop on the tour in Las Vegas, a man asked Bush how he would be a different president than his father and brother were. He deflected by turning the question around at the crowd.

“You have brothers and sisters?” he asked the man.

“Yes,” the man said.

“Are you exactly the same?” Bush asked.

“No!” people shouted back in response.

Most Bush appearances last about an hour. He poses for a few pictures and shakes hands before giving about seven minutes of introductory remarks. Then he fields questions for at least 45 minutes on immigration, energy policy, Common Core education standards, Alzheimer’s research or the national debt.

He traveled Thursday to the Georgia State Capitol in Atlanta for a brief stop, which coincided with a visit by Georgia-born rapper Ludacris, who was being honored for his charitable foundation.

Bush joked that he came “because I heard Ludacris was gonna be here.” Photos of Bush and Ludacris circulated widely on Twitter.

Repeatedly during events this month, Bush marveled about the future. Pointing to the Pebble Smartwatch on his wrist, Bush said most Americans will soon be wearing such devices to track their health, bank accounts and sleep patterns — part of a “technological revolution,” as he put it in both New Hampshire and South Carolina.

Bush is 6-foot-4, a few inches taller than his brother. He has a slight hunch in his shoulders, something he admitted he’s working to correct. He has lost more than 20 pounds in the past few months as he prepares for the expected campaign. Audience members commonly say that he’s much taller than they expected.

While talking with voters, he calls men “brother,” says he’s “all in” on his positions and frequently labels things “cool.” He goes out of his way to thank Hispanic waiters at restaurants and speaks to them in his fluent Spanish. He uses outdated expressions such as “Holy schnikes” and “Holy Toledo,” and decries the “yapping” and “food fight” in Washington.

He also has a dry, deadpan sense humor — so dry it often evaporates quickly. “There are some people that have been dying to ask a question back there,” he told the Las Vegas crowd. “I don’t want them to do that.”

At this early stage, most of Bush’s public appearances are hastily arranged. In the hotel ballrooms, community centers and restaurants, there are no campaign placards, no booming music, no bright T-shirts and very little staff. Sometimes, he’s showing up as the headline act at somebody else’s event, such as a Chamber of Commerce meeting.

His traveling posse includes similarly lanky, bespectacled men. There’s Josh Venable, who worked for Bush’s education foundation and advises him on policy matters. Coleman Lapointe is the “body guy” who once worked for Bush’s father and is tasked with taking photos on the cellphones of supporters. Tim Miller, Bush’s communications director-in-waiting, is the freshest face in the pack.

Other traveling companions have included Kristy Campbell, his press secretary who held a similar job when he was governor; Sally Bradshaw, a longtime consigliere tasked with recruiting top staffers and donors; and David Kochel, his campaign manager-in-waiting.

In each state, the group piles into a rented SUV and Bush sits in the front passenger-side seat — never in the back. He snacks on unsalted almonds as part of a strict “paleo” diet. That meant eating takeout from Ruth’s Chris Steak House on the ride from ­Columbia to Myrtle Beach on Tuesday night, or pulled pork with no barbecue sauce during a recent stop in Waukee, Iowa.

Virtually all the voters who show up to see Bush say they are reserving judgment until they see other candidates.

“I want to know more about him,” Dennis Cavanaugh of Murrells Inlet, S.C., said after Bush’s visit to Myrtle Beach. Cavanaugh said that after Obama, the country needs to do a better job vetting the next president. “Anybody and his brother can run for office — literally. I think that’s part of what the big problem is.”

His wife, Anne, seemed won over by Bush for a simple reason: He encouraged people to e-mail him questions to his personal address, jeb@jeb.org.

“I like that because I think if I e-mailed President Obama I wouldn’t get an answer,” she said.

As his travels continue, Bush seems increasingly convinced that he can outlast others in the field.

“It’s been a blast,” he told reporters late one day in Columbia. “Just for the record, I’m not a candidate — but as I’ve gone about listening to people and hearing their questions, it’s been fun, truly it has been joyful.”