Though most of the conversation takes place off screen, Trump was wearing a microphone and cameras were rolling when he spoke about his attempts to seduce women.
"I did try and [expletive] her. She was married," he said in the video. "I moved on her like a [expletive], but I couldn't get there. And she was married."
Trump and Bush also made comments about Arianne Zucker, the Days actress who escorted them on to the show's set.
"Your girl's hot as [expletive], in the purple," Bush said about Zucker.
"I've got to use some Tic Tacs, just in case I start kissing her," Trump said. "You know I'm automatically attracted to beautiful -- I just start kissing them. It's like a magnet. Just kiss. I don't even wait."
"And when you're a star, they let you do it," he added. "You can do anything. Grab them by the pussy. You can do anything."
Friday night, Trump issued a video apology on social media, saying, "these words don't reflect who I am."
"I said it, I was wrong, and I apologize," he said.
At the end of the video, Trump turned the focus to Bill and Hillary Clinton.
"I've said some foolish things, but there's a big difference between the words and actions of other people," he said. "Bill Clinton has actually abused women, and Hillary has bullied, attacked, shamed, and intimidated his victims. We will discuss this more in the coming days."
Clinton commented on the video via Twitter saying, "This is horrific. We cannot allow this man to become president."
This is horrific. We cannot allow this man to become president. https://t.co/RwhW7yeFI2— Hillary Clinton (@HillaryClinton) October 7, 2016
Trump's wife, Melania, also released a statement through Trump's campaign on Saturday afternoon. In it, she urged Americans to accept his apology.
"The words my husband used are unacceptable and offensive to me. This does not represent the man that I know. He has the heart and mind of a leader. I hope people will accept his apology, as I have, and focus on the important issues facing our nation and the world."
The couple married less than a year before the video was recorded.
Trump and Clinton will face off in the second presidential debate at 9 p.m. Sunday.