Earlier in the conversation, Trump recalls talking about trying to woo a married woman.
"I moved on her actually, she was down in Palm Beach and I failed. I'll admit it. I did try to fuck her, she was married ... and I moved on her very heavily," Trump is heard saying.
"I took her out furniture shopping. She wanted to get some furniture and I told her 'I'll show you where you can get some nice furniture,'" Trump is heard saying. "I moved on her like a bitch, and I could not get there, and she was married. And all the sudden I see her and she's got the big phony tits, she's totally changed her look."
In a prepared statement, Trump responded to the clip.
"This was locker room banter, a private conversation that took place many years ago. Bill Clinton has said far worse to me on the golf course — not even close. I apologize if anyone was offended."
RNC chairman Reince Preibus also responded to Trump's comments in a statement Friday night.
"No woman should ever be described in these terms or talked about in this manner," he said. "Ever."
Bush, now with the TODAY show, apologized in a statement Friday night, and said he was playing along in the 2005 conversation.
"Obviously I'm embarrassed and ashamed. It's no excuse, but this happened eleven years ago — I was younger, less mature, and acted foolishly in playing along. I'm very sorry," Bush said in the statement.
The new revelations come just 33 days left before the election, making Trump's uphill climb with women voters even more challenging.
Just 24 percent of women view Trump favorably, according to the latest NBC News/ Wall Street Journal poll from mid-September. In a two-way race, Trump polls two points higher with men, while Clinton leads Trump with women by 14 points.