It appeared that Mr. Bush was Michael Phelps' lucky charm as he went to the Water Cube for the second straight day to watch the American swimmer's pursuit of Mark Spitz's record of seven gold medals. The president witnessed a stunning comeback as the 400-meter freestyle U.S. relay team rallied to win, giving Phelps his second gold and second world record here.
But Moscow's military offensive in the former Soviet republic of Georgia was always looming in the background. In an interview with NBC Sports, Mr. Bush criticized the violence, calling it unacceptable and Russia's response disproportionate.
The United States is waging an all-out campaign to get Russia to halt its retaliation against Georgia for trying to take control of the breakaway province of South Ossetia.
"I've expressed my grave concern about the disproportionate response of Russia and that we strongly condemn the bombing outside of South Ossetia," Mr. Bush said. He said he did so directly to Prime Minister Vladimir Putin before the opening ceremonies Friday - Putin left China the next day - and by phone to Russian President Dmitri Medvedev.
Vice President Dick Cheney told Georgia's pro-American president that "Russian aggression must not go unanswered, and that its continuation would have serious consequences for its relations with the United States," Cheney's office reported Sunday.
Still, the Olympics went on, and Mr. Bush took advantage of his final hours in Beijing, going to the Water Cube to watch the swimming. He sat in the VIP area with wife Laura on one side, daughter Barbara on the other. Former Republican presidential candidate Mitt Romney and his wife were sitting in front of them, and Microsoft founder Bill Gates was right behind.
When photographers swung by to snap a few pictures, the president picked up a small U.S. flag and waved it proudly.
The former co-owner of the Texas Rangers was clearly in his element as he took in a practice game between the U.S. and Chinese men's baseball teams. He posed for a photo with both teams - the Americans in blue jerseys, the Chinese in red - before telling them: "Good luck. Play hard. Play hard."
The president threw out the first pitch three times, appearing to miss the strike zone each time. His family and staff applauded when he went to the stands.
In an interview with The Associated Press just before leaving Beijing, Mr. Bush said the Olympics exceeded his expectations, calling them a "very uplifting experience" that he won't forget.
"The whole thing is genuine," Mr. Bush said. "That's the good thing about the Olympics."
He also said his attendance, which has been criticized by human-rights activists as endorsement of China's repression of free expression, was important.
"It's good to send a signal to the Chinese people that we respect them, that this is about their country," Mr. Bush said.
Mr. Bush used the visit to press President Hu Jintao over China's jailing of political and religious activists. In the NBC interview, he was asked if the message is getting through.
"It's hard to tell," Mr. Bush replied. "He listened politely. I can't read his mind, but I do know that every time I met with him I pressed the point."
Mr. Bush reflected on an Olympics experience that was extraordinary even by presidential standards.
"It's exceeded my expectations," Mr. Bush told The Associated Press in an interview Monday before returning to Washington. He meant the whole deal: the venues, the people, the pride.
Never before had a U.S. president taken part in an Olympics on foreign land. Mr. Bush came and soaked it in for four days.
He managed to do what he promised he would - take in a whole lot of sports - while dealing with Russia's violent crackdown on Georgia and carefully confronting China's repression of human freedoms.
At the Olympic baseball stadium, Mr. Bush was in the mood to talk sports, not policy. He had just spent time mingling with the Chinese and U.S. baseball teams, and now they were lacing line drives across one of Beijing's pristine Olympic venues.
The president was in his element.
"I think the highlight was getting my picture taken with the teams," Bush said, referring to a moment he had with the whole U.S. Olympic contingent.
The comment was surprising and telling. Mr. Bush gets his photo taken so often with so many groups that it would hardly seem to be a defining moment. Consider, for example, that he also got to see the stunning opening ceremony and an exhilarating victory by U.S. swimmers.
But for Mr. Bush, those seemingly routine photo opportunities with athletes are a joy. Anyone close to him knows he likes sports for what they are, but also for what they represent: competition, grit, work. It doesn't hurt that the athletes are thrilled to see him.
"They were so gracious, and grateful, and excited," Mr. Bush said. "It's just a very energetic feeling. You know, they represent the best of U.S. athletics. And they were really excited about their events, and they're full of hope. It was just a very uplifting experience."
And he was everywhere.
Mr. Bush went to a practice of the U.S. softball team, as well as the baseball practice game, as a sign of support for the two sports. Both were cut from the Olympic program in 2012.
The president got sandy practicing with the beach volleyball duo of Misty May-Treanor and her partner Kerri Walsh. A photo showing Walsh's show of spirit - she prodded the president to give her a playful smack on her lower back, and he went along - caused something of a buzz.
Mr. Bush said he saw no reason why.
"I didn't take it very seriously," he said. "I guess everything the president does is interesting."
When Mr. Bush and his dad, the former president, were making a pre-game visit to the U.S. men's basketball team, CBS News correspondent Mark Knoller reports that Lebron James was heard to greet former President Bush with the words: "What's up, pops?"
Before the big U.S.-China basketball game, Mr. Bush met the players, huddled up, and led them in a one-two-three-USA cheer. He laughed in describing the moment, how high he had to look up to see their faces.
Mr. Bush figured the crowd at the game would be raucous, and didn't know why it wasn't.
"And then it dawned on me that they're neutral," Mr. Bush said. "It's an international games. There are people from all over the world watching and not cheering madly."
He did, though.
In a fine bit of timing, the last official competition the president caught was so good that within minutes it was being described as one of the greatest comebacks in Olympic history.