"When I ran for office, I said he is a chaos candidate and would be a chaos president," Bush said on Friday.
"Unfortunately, so far chaos organizes the presidency right now," he said, speaking at the annual SALT hedge fund conference, which is headlined by bigwigs from the world of politics, finance, sports and entertainment.
Bush said it appears the Trump administration is "living in the tyranny of the moment" instead of "executing on a clear agenda."
Even though Bush acknowledged he's not on Trump's "speed dial," the former 2016 GOP rival of the president offered some unsolicited advice for calming things down in the White House.
"Stop tweeting," Bush said.
The former Florida governor and Republican presidential candidate acknowledged there are benefits to Trump's Twitter habit, including bypassing the media to get his message directly to millions of people.
But Bush warned that Trump's tweetstorms give "our enemies all sorts of nuances and insights" into the mind of the commander in chief.
The other problem he says is that the administration lacks discipline when it comes to speaking to the press.
"I've never seen a White House as leaky as this one," Bush said. "People should be fired if they're disloyal to the president of the United States and leaking."
Bush did give Trump some credit, saying he made some "really good appointments," including Supreme Court Justice Neil Gorsuch.
He also thinks the appointment of former FBI Director Robert Mueller as a special counsel on the Russia investigation could be a "good thing" for Trump by allowing the White House to get back to business. (Bush praised Mueller as a "person of incredible integrity" and appointing a special counsel was necessary.)
One area of business Trump wants to refocus on is repealing and replacing Obamacare. But Bush said he doesn't believe Trump will get health care reform through Congress this year.
Sitting next to Bush on stage, former top White House adviser to President Barack Obama, Valerie Jarrett, criticized the all-male working group writing the health care reform bill in the Senate.
Bush agreed, saying his experience shows that having diverse input can help avoid "really stupid mistakes."
"When you have 10 overage white guys looking at things, there's better than a 50/50 chance it's going to be a screw-up," Bush said to laughter.
Trump's early stumbles are already turning attention to 2020.
Jarrett surprised the audience by saying she believes former Massachusetts Gov. Deval Patrick will be the next Democratic nominee for president.
Bush picked Joe Biden, citing the former vice president's Thursday night appearance at SALT where he didn't rule out a run.
Asked if Trump will face a Republican challenger in 2020, Bush said: "It's hard to tell. It's too early."