Bush, who has been Trump's most consistent campaign-trail critic, blasted some of his GOP competitors for not similarly going after Trump.
"It's ridiculous," Bush said after suggesting his opponents were scared of Trump.
"The guy's just a real-estate guy," Bush continued. "He's gone bankrupt four times. He's a successful man but he's not perfect by any stretch of the imagination. So why not confront him and challenge him?"
The MSNBC show then played a word-association game with Bush. The first word: "Trump."
"Loser," Bush replied without hesitating.
Trump, the Republican presidential front-runner, called into "Morning Joe" for a subsequent interview. Trump fired back at Bush, whom he repeatedly called a "stiff."
"Jeb is an interesting duck," Trump mused. "Here's the story on Jeb: He's a stiff who you wouldn't hire in private enterprise, OK? This is a stiff. This is a guy that if he came looking for a job, you'd say: 'No thank you.' And that's the way it is."
After accusing Bush of lying about his record, Trump added:
The guy's a total stiff. He's not going anywhere. Remember this - for the voters - he wants Common Core and he's very weak on immigration. Remember, … he said, "They come to our country through the act of love." Jeb is weak on immigration.
Both Bush and Trump have been focused on Tuesday's primary in New Hampshire.
Watch the two candidates attack each other on 'Morning Joe' below:
.@realDonaldTrump responds to @JebBush calling him a 'loser': Jeb Bush is 'a total stiff' https://t.co/6TwPNvQJP9
- Morning Joe (@Morning_Joe) February 8, 2016
.@realDonaldTrump responds to @JebBush calling him a 'loser': Jeb Bush is 'a total stiff' https://t.co/6TwPNvQJP9
- Morning Joe (@Morning_Joe) February 8, 2016