"This is going to come as quite a shock to people up here that I can write a book, much less read one," the former president said, according to Politico. Mr. Bush is currently working on a memoir.
He also reportedly told an audience of administration alumni that Cheney, who had planned to come to the meeting, was not able to attend following his recent heart attack. He said the former vice president is "feeling well" and "has a fierce constitution."
Added Mr. Bush: "I have no desire to see myself on television. I don't want to be a panel of formers instructing the currents on what to do...I'm trying to regain a sense of anonymity. I didn't like it when a certain former president -- and it wasn't 41 or 42 -- made my life miserable."
That appears to be a shot at former President Jimmy Carter (#39), who said back in 2006 that the Iraq war had been "a flat disaster" and that the Bush administration "and particularly the vice president and the secretary of defense have, I think, quite often deliberately misled the American people about the danger in Iraq to begin with, the causes for going to war in Iraq, and they have also misled the American people about what is happening in Iraq since we invaded."
Carter was also exceedingly critical of Cheney and called the Bush administration the "worst in history" from the perspective of its "adverse impact on the nation around the world," though he later walked back that comment as "maybe careless or misinterpreted."
The former president and vice president have taken diverging paths since leaving the White House, with Cheney making high-profile criticisms of the Obama administration as Mr. Bush has largely stayed out of the spotlight, saying Mr. Obama "deserves my silence." Last week Cheney suggested that Mr. Obama would be a one-term president.
Cheney has also indicated he disagreed with some Bush administration decisions, including the trial of terror suspects in civilian courts and the lack of a full pardon for former Cheney chief of staff Lewis "Scooter" Libby following the Valerie Plame scandal.
Cheney, like Mr. Bush, is working on a memoir.
The Bush-Cheney Alumni Association, which hosted Friday's breakfast, is the new name for Bush-Cheney 2004 Inc., the organization that ran Mr. Bush's reelection campaign.
It is "devoted to furthering the ideas and principles of the Bush-Cheney Administration with the hope that they will continue to positively impact our nation and the world for years to come," according to an email to supporters reported by the Wall Street Journal.
At the breakfast, Mr. Bush said for the first time he approved of Cheney's post-White House role, saying, "I'm glad Cheney is out there."
As Politico reports, he also said No Child Left Behind was "the most advanced civil rights legislation since the Voting Rights Act." And he warned against "swagger," saying "sometimes I got carried away rallying the country."