The US president was talking privately on Monday to Tony Blair, the British prime minister, during a lunch at the Group of Eight summit in St Petersburg about an upsurge of violence in the Middle East.
Neither immediately realised a microphone was transmitting their candid thoughts on that and other issues on the summit's official television network.
Bush, eating a piece of bread and calling for a diet Coke, said: "I think Condi [Condoleezza Rice, the secretary of state] is going to go [to the Middle East] pretty soon."
Blair replied: "Right, that's all that matters, it will take some time to get that together."
"I'm just going to make it up. I'm not going to talk too damn long like the rest of them. Some of these guys talk too long"
Rice said on Sunday she was thinking of going to the region if it would help.
Blair said: "See, if she goes out she's got to succeed as it were, where as I can just go out and talk."
"See, the irony is what they need to do is get Syria to get Hezbollah to stop doing this shit and it's over." Bush replied, without specifying who "they" are.
Bush also seemed to complain about Kofi Annan, the UN secretary-general, wanting an immediate ceasefire to stop the violence between Israel and Hezbollah.
"What about Kofi Annan? I don't like the sequence of it. His attitude is basically ceasefire and everything else happens," Bush said.
Blair said: "What does he think? He thinks if Lebanon turns out fine, if he gets a solution in Israel and Palestine, Iraq goes in the right way, he's done it. That's what this whole things about. It's the same with Iran."
But Blair also said that "the thing that is really difficult is you can't stop this unless you get this international presence agreed".
A G8 statement on Sunday suggested the UN Security Council should consider an international security and monitoring presence on the Lebanon-Israel border, an idea Blair is pushing.
Later, Bush said he felt like telling Annan to telephone Bashar al-Assad, the Syrian president, "and make something happen".
"We're not blaming Israel and we're not blaming the Lebanese government," he said.
The two leaders also appeared to chat about the stalled Doha Round of world trade talks.
"I just want some movement," Bush said, to which Blair replied: "It may be that it's impossible."
Later, plans were announced for ministers from six key trade powers to meet in Geneva from Monday to try to unblock the talks.
"What does he [Kofi Annan] think? He thinks if Lebanon turns out fine, if he gets a solution in Israel and Palestine, Iraq goes in the right way, he's done it. That's what this whole things about. It's the same with Iran"
Ultimately Blair noticed the microphone and hastily switched it off, but not before the recording had reached news media.
In the chummy conversation between long-time allies, Bush teased the British leader about a sweater Blair had apparently given him.
"Thanks for the sweater, it was awfully thoughtful of you. I know you picked it out yourself," Bush said.
"Oh, absolutely," said Blair.
Bush also said that when he next spoke to G8 leaders, he would keep it brief.
"I'm just going to make it up. I'm not going to talk too damn long like the rest of them. Some of these guys talk too long. Gotta go home. Got something to do tonight," he said.
Bush also made quite a bit of small talk with other leaders about how long it takes to get home after a summit like this.
"I gotta leave by 2.15. They want me out of town so they can free up your security forces," he said, apparently to the Russian president Vladimir Putin, who was not seen.
"This is your neighbourhood – doesn't take you long to get home," he told another leader, who was off camera.
"Russia's a big country, you're a big country," he told another.