Mr. Bush has become part of the Dallas firmament again, a regular at restaurants around town and host of barbecues at home. He helped raise a reported $1.2 million for the M. D. Anderson Cancer Center. He is expected to attend a Dallas event on Monday honoring the columnist and Fox News commentator Charles Krauthammer. “Clinton is a citizen of the world,” said a friend, “and Bush is a citizen of Dallas.”

That is not to say that Mr. Bush does not revisit the consequential days in the White House. From time to time, there are revealing moments, friends say.

“You’re leaving as one of the most unpopular presidents ever,” a former aide noted during a visit to Dallas shortly after Mr. Bush’s return. “How does that feel?”

Mr. Bush pushed back: “I was also the most popular president.”

Today, Mr. Bush finds himself somewhere in the middle. A Gallup survey found that 49 percent of Americans viewed him favorably, compared with 46 percent who saw him unfavorably, hardly as high as Mr. Clinton or Ronald Reagan but the first positive balance in eight years.

That reflects a return to the fold by some conservatives who see Mr. Bush more positively than Mr. Obama and perhaps a softening by some moderates and liberals who see him more positively than Tea Party Republicans. Former Bush aides seem less defensive today because Mr. Obama adopted much of his predecessor’s security policies and because the current president has had his own troubles.

“There’s now more appreciation and even some nostalgia for his resolve, the clarity of his convictions; things that were sometimes seen as liability when he was in office are now looked at with more affection,” said William C. Inboden, a former aide and the executive director of the Clements Center on History, Strategy and Statecraft at the University of Texas, Austin. “There’s also more appreciation for the challenges and the calls a president has to make to keep a nation safe.”

Mr. Bush has benefited from his decision not to publicly second-guess his successor. Donna Brazile, who managed Al Gore’s campaign against Mr. Bush in 2000, said she was told that Mr. Obama was “grateful and admiring of how the Bushes approached the post-presidency,” adding that “this should serve as a different template for the modern presidency.”