By the end of the night, Bush had even told Trump to put on his "big boy pants."
In their most substantive policy dispute, the two disagreed sharply over whether refugees who fled the Middle East amid ISIS' rise should be allowed in the United States.
"I think we're duty-bound to provide support," Bush said in Bedford.
Down Route 101 in Keene, Trump called the refugees a "tactical ploy," suggesting that "they could be ISIS, I don't know."
"If I win, they are going back," he said.
It was a split-screen display of the dramatic contrasts in style and substance between the two Republican presidential contenders -- Trump a front-runner touting his outsider credentials; Bush an establishment favorite linked to his brother's foreign policies.
Bush lashed out at Trump's bombastic approach to politics, saying that "my mother would whack me across the ears" if he followed suit.
"If you're looking for the big guy on the stage, talking in the first-person, singular, 'I, I, I, me, me, me it's all about me,' I'm not good at that," he said.
He accused Trump of "big-dog, loud-talking, insulting leadership."
"My energy comes from helping people have a chance to live the lives that the want. ... The kind of leadership we need is servant leadership," he said.
Bush added: "You don't win by telling people how stupid they are."
An hour west of Bush's event, Trump was mocking Bush, one of his favorite targets, over their respective draws.
"Jeb Bush is down the road tonight," he says. "They're expecting 150 people."
(Bush's campaign says their attendance was about 200).
Trump said the fire marshal had told him there were 3,564 people on hand for his event in Keene on Wednesday evening -- and there would have been more, but he wasn't allowed to cram people into the aisles.
"And it's always like this, by the way," he said.
Trump also said he doesn't buy the idea that Bush and Marco Rubio -- who worked together in Florida, when Bush was older governor and Rubio was the new House speaker -- are actually friends.
Behind the compliments, Trump said, "They hate each other."
"It's political bulls***," he said.
With reporters after his event, Bush pushed back against Trump's characterization of his relationship with Rubio.
He said that "Marco can put his big boy pants on. I know I can ... We're friends. I can take criticism. He can as well."
Then, he lashed out at Trump.
"Donald seems to have a harder time taking criticism. And he probably needs to put on his big boy pants too," Bush said. "He's running for president of the United States. He ought to take a little incoming. He's great at giving it out."
Bush added: "Donald Trump has no knowledge about my relationship with Marco Rubio."