The conversation between Kyra Phillips and another woman was clearly heard as Mr Bush talked in New Orleans to mark the anniversary of Hurricane Katrina.
During the chat, Ms Phillips talked about her husband and called her sister-in-law a "control freak".
CNN apologised to viewers and the president, citing "audio difficulties".
'Handsome and loving'
The gaffe happened when Ms Phillips' microphone remained on during a brief break from the set of the daily news programme Live From.
The programme was broadcasting Mr Bush's speech live from New Orleans, but viewers also heard about 90 seconds of the anchorwoman's conversation during what has been described as a bathroom or hair and make-up break.
Her comments, which were at first muffled but then became clearer, started with an apparent expletive, before turning to praise of her husband in a conversation about men.
"Yeah, I'm very lucky in that regard with my husband. My husband is handsome and he is genuinely a loving, you know, no ego... you know what I'm saying," she was heard telling the other woman, whose identity is not known.
"Just a really passionate, compassionate, great, great human being. And they exist. They do exist. They're hard to find... But they are out there."
'Protective'
Shortly afterwards she was heard laughing, before talking about her brother.
"I've got to be protective of him," she said. "He's married, three kids and his wife is just a control freak."
At that point, another woman's voice is heard cutting in, telling Ms Phillips to turn off her microphone as her conversation had been on the air, and the broadcast chat ends.
CNN issued a statement apologising for the error, and also apologised to the White House, Reuters news agency reported.
"CNN experienced audio difficulties during the president's speech today in New Orleans," the statement said.
"We apologise to our viewers and the president for the disruption."
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