Event moderator, billionaire David Rubenstein, asked the two at the scholastic leadership event in Dallas about what they viewed as the most important quality for someone who wants to be President. Both stressed the virtue of humility.
"I think it's really important to know what you don't know and listen to people who do know what you don't know," Bush said.
Clinton -- who, like Bush, didn't mention President Donald Trump -- agreed that officeholders need to be humble, and warned that those "who are real arrogant in office" have forgotten that history will be their judge.
"If you want to be President, realize it's about the people, not about you," Clinton said. "You want to be able to say, 'People were better off when I quit.' ... You don't want to say 'God, look at all the people I beat.'"
Clinton and Bush have developed a friendship over the years, especially as Clinton and former President George H.W. Bush collaborated in their post-presidential periods. During the conversation, the two chummily exchanged compliments and light-hearted barbs.
Clinton complimented his successor on immigration in relation to current members of the Republican Party.
"I told George once a year or so ago, I said I hope you're not the last Republican president who's not afraid of immigrants," Clinton said.
Clinton also spoke at length about his concern over political polarization and people only seeking information corresponding to their ideologies. He said it bothers him more than anything else when it comes to his concerns about the future.
"We don't want to be around very many people who disagree with us normally," Clinton said. "We get news in silos."
He argued that this perpetuates political stagnation.
"We all vote for the gridlock we say we hate," Clinton said.
The rapport between the two, many years removed from political office, came as a stark contrast from the massive political fights they grappled with during their presidencies and the contemporary political climate. They attributed part of their close relationship in the face of partisan differences and competition to gracious personal behavior between them personally.
"When I left office, I told him, I said if I can ever help you, I'll do it," Clinton said. "If I can't in good conscience, I won't, but I'll never embarrass you in public. And you know (my wife Hillary Clinton) was a senator. I said I may have to make some comment that disagrees with some policy of yours, but I will always do it respectfully, and I want you to succeed."
Clinton added that he viewed working with Bush's father "one of the great gifts" of his life.
Likewise, Bush said part of his affection for Clinton came from Clinton's humble victory over his father in 1992.
"I think it starts with Bill Clinton being a person who refused to lord his victory over Dad," Bush said. "In other words, he was humble in victory, which is very important in dealing with other people."