Bush wrote in a New York Times opinion piece about Trump's "grab them by the pussy" comment made on a hot mic in an "Access Hollywood" bus in 2005.
Bush accused Trump of engaging in "revisionist history" amid reports the president was questioning the authenticity of a recording featuring the lewd comments leaked just a month before the November 2016 election.
"He said it," Bush wrote in a New York Times opinion piece about Trump's "grab them by the pussy" comment made on a hot mic in an "Access Hollywood" bus in 2005.
"And we laughed along, without a single doubt that this was hypothetical hot air from America's highest-rated bloviator," said Bush, who was fired from NBC's "Today" after the tape surfaced last year.
Offering an explanation about why he did not take action upon hearing the crude boasts of assault, Bush added: "There were seven other guys present on the bus at the time, and every single one of us assumed we were listening to a crass standup act. He was performing. Surely, we thought, none of this was real."
However, he added, "we now know better," referring to women who have come forward to accuse Trump of unwanted sexual advances.
Trump won the election despite the outrage triggered by the recording.
But that was before the watershed moment of reckoning America is now experiencing after scores of sexual assault and harassment claims have felled entertainment, political, media and business leaders who abused their positions of power.
At the time of the tape's release, Trump dismissed the comments as "just words" and "locker room talk," and denied the sexual assault allegations, threatening to sue his accusers after the election.
The New York Times and The Washington Post reported in recent days that Trump had supporters and at least one senator that it may have been faked, and that the voice was not his.
Bush, a nephew of former president George H.W. Bush, said he believed the women accusing Trump.
"President Trump is currently indulging in some revisionist history... "This has hit a raw nerve in me," Billy Bush said.
"I can only imagine how it has reopened the wounds of the women who came forward with their stories about him, and did not receive enough attention."
Bush noted that at the time of the recording, he was only in his first year of co-anchoring NBC's "Access Hollywood," while Trump was "the network's biggest star" due to his role on "The Apprentice."
"To these women: I will never know the fear you felt or the frustration of being summarily dismissed and called a liar, but I do know a lot about the anguish of being inexorably linked to Donald Trump," Bush added.
"You have my respect and admiration. You are culture warriors at the forefront of necessary change."