In his campaign announcement speech last month, the billionaire questioned Bush's intelligence, before asking the crowd: "How the hell can you vote for this guy?"
Trump has beat up on Bush more than any of the other candidates in the GOP field: In a sit-down with CNN's Anderson Cooper last week, his derided Bush's policies as "weak" and a "total disaster."
And earlier this month, Trump took a more personal jab, retweeting the message: "#JebBush has to like the Mexican Illegals because of his wife." (Trump later said he didn't authorize the tweet but that he certainly doesn't regret it).
Bush supporters say they are unconcerned about the attacks, at least so far. Some even argue that the contrast between Bush, a seasoned politician with a reserved demeanor, and Trump, a bull-in-a-china-shop ex-reality TV star, is helping to make Bush more presidential.
"I think it actually helps Jeb in the long run that a crazy son of a bitch is after him all the time," said Mac Stipanovich, a Florida lobbyist and longtime Bush supporter. "You can tell more about a man by his enemies than his friends, and if you want to have an enemy in presidential politics, let it be Donald Trump."
But Trump allies say that the worst may still be ahead for Bush.
Trump's close associates — all of whom spoke anonymously with CNN to share his private thinking — said his preoccupation with Bush has been years in the making. His grievances, they said, go beyond policy disagreements with Bush over issues like the Iraq War, immigration and Common Core.
Described by friends as intensely competitive, Trump has a deep aversion to the idea of a dynasty candidate who might feel entitled to the party's nomination. Privately and publicly, Trump is known to refer to Bush as "a stiff," believing that the country badly needs a candidate who can energize the base and that Bush simply "is not a cheerleader," one person in Trump's inner circle said.
"For some reason they didn't hit it off. Their styles are totally different," one Trump friend said.
Trump's animosity towards Bush in 2015 may come as a surprise to those who remember that years ago, the two men seemed to enjoy a friendlier relationship.
In the late 1990s, the real estate mogul fundraised for Bush's gubernatorial campaign in Florida. And in his 2000 book, Trump referred to Bush as a "good man," describing him as "bright, tough, and principled," Buzzfeed reported.
Trump's campaign manager Corey Lewandowski downplayed questions about how Trump's past support for Bush squares with his recent criticism.
"Trump gives money to everybody, right? All politicians — and I'll give you his exact quote — 'kiss his ass,'" Lewandowski told CNN. "So it's not a big surprise that Mr. Trump has donated to politicians for the last 30 years because politicians are easy."
In the crowded GOP field, Trump has emerged by far the most aggressive candidate when it comes to attacking other Republicans. He has called former New York Gov. George Pataki a "terrible governor" who "couldn't be elected dog catcher if he ran again"; blasted former Texas Gov. Rick Perry for failing to control the border; and labeled Rubio "extremely weak" on immigration.
But Bush seems to be in a category by himself.
On the campaign trail, Trump is using the former governor to highlight his own policy priorities.
He's gone after the way Bush handled questions about the Iraq War — which Trump describes as one of the biggest blunders of George W. Bush's presidency.
"It took him five days to answer the question on Iraq. He couldn't answer the question," the real estate developer boomed at his campaign launch. "I said, 'Is he intelligent?'"
There is perhaps no other issue that Trump has spoken more passionately about as a candidate than immigration. He's vowed to build an "impenetrable" wall along the country's southern border and sparked national outrage by saying that "criminals" and "rapists" were entering the U.S. from Mexico.
Bush is "weak" on immigration and his views are likely influenced by the fact that his wife is from Mexico, Trump told Cooper.
Bush, who has repeatedly denounced Trump's immigration comments, has shrugged off Trump's viability as a candidate.
"I don't know if he's having success. We'll see in the long haul," Bush told Fox News last week, adding that the party should not focus on "someone who I doubt will be president and is not a constructive force for our party."
A Bush spokesperson told CNN that the ex-governor is "focused on his message and connecting with people around the country."
Iowa State Sen. Charles Schneider, a Bush backer, offered this theory for why Trump is singling out the ex-governor: "Generally speaking, you don't see someone get attacked by their fellow Republicans unless they are someone who's sitting at the top of the field and who someone else is trying to tear down."