"With Trump, it's not much of a give-and-take," Bush said. "When he said what he said at the end ... to me, it was more braggadocio — his word — and performance."
The tape, which was reportedly recorded while Trump and Bush were arriving on the set of "Days of Our Lives" in 2005, captures Trump and Bush — at the time the star of "The Apprentice" and a host of "Access Hollywood," respectively — in the midst of a vulgar exchange, with Trump bragging about his ability to grope women because he's "a star."
After the tape's release, Bush's career came to a screeching halt. He was fired from his job as a co-host of "Today," and he has been unemployed since then. Trump went on to win the presidency.
"The irony is ... glaring," Bush told ABC News.
Asked if he thinks he should have been fired, Bush said, "I understand people's reaction. I agree. I also felt that way."
He told ABC News that he has not spoken to Trump since the tape's release.
"There was no relationship there," Bush said. "It was ... work related. And I interviewed him multiple times, especially back then. He never reached out ... and I didn't reach out."
Bush said that after the exchange with Trump, "I reported it as soon as it happened."
"I said, 'You wouldn't believe the things that Trump was saying, you know, off camera,'" Bush said.
He added that he found out days after the incident that it was recorded, "I said, 'Oh, my gosh, wow.' But I never thought about it again. I just went on. It was Trump.
"It was an inconsequential ... He wasn't running for president. He was, at the time, the biggest star on television."
Bush told Roberts that he didn't listen to the tape "until just days before the rest of the world got it."
"And I recoiled ... It was guttural," Bush said of his initial reaction to hearing the recording. "Nobody reacted harsher and more gutturally than I did ... It really, really just killed me."
"I remember the guy on the other side ... Twelve years ago, it was my first year as co-host of the show," he said. "I was insecure ... I was a pleaser."
"I kind of remember wanting these celebrities to like me, so that I could keep going ... in this job," Bush said.
He acknowledged that wanting to prove himself is no excuse for his actions, saying, "I should have known better, absolutely. There's no question about that."
"People also say, 'You should have stopped it,'" Bush said. "I didn't have the strength of character at the time to do that. I wish I did."
Bush told Roberts that his wife remained supportive "the whole way through" in the aftermath of the tape's release.
"She was very understanding," he said. "She knows very well the man she married and who I am."
He said he hopes to get back to work soon, adding that he feels he is a "changed person."
"I am only ready to get back to work now because there is purpose and there is clarity and there is acceptance and there is a changed person," Bush said.
"I do feel like a better man," he said. "I feel like ... a better father, partner, friend. And, I do think, better at my job than I ever was."
He offered advice to young men entering the industry, saying, "Do not doubt yourself. Stay true to who you are."
"I sacrificed, you know, my own dignity in that moment. I was very pleased to say goodbye to that guy," Bush said.