Bush was suspended from his co-hosting duties on the 9 a.m. hour of "Today" after the footage from Trump's conversation with him became public last week.
During the taping of a segment for "Access Hollywood," the future Republican presidential nominee makes lewd comments about women as Bush, then a host of the program, responds and laughs.
Bush quickly issued an apology in the wake of the controversy.
"It's no excuse, but this happened 11 years ago -- I was younger, less mature, and acted foolishly in playing along," he said in a statement. "I'm very sorry."
Kristine Bell of "Frozen" fame pointed out the disparity between Bush's punishment and Trump's continuing presidential bid.
"So Billy Bush was suspended from @TheTodayShow &we may nominate the other guy on the tape to run the free world," Bell tweeted. "AM I IN THE TWILIGHT ZONE?!
Actress Jamie Lee Curtis cautioned in a tweet, "Let's not just throw deleted account Billy Bush who is not running 4 president under the (bus) It is @realDonaldTrump whose comments r repugnant."
Former CNN host Piers Morgan also stood up for Bush.
"As Billy Bush gets shredded by US media, I'd like to say I've known him 10yrs & always found him to be a good guy & excellent broadcaster," Morgan tweeted.
Kit Hoover, who worked with Bush on "Access Hollywood," said Monday on the show that "those tapes were a decade ago and it was seven minutes of someone's life, and all I can tell you is what I know and the person that I sat next to for the last six years, and that person for me is a totally different person."
"He always treated me with kindness, such respect. ... He treated me like an equal from day one, and I think anybody that watched our show at home and saw us together knew how much he rooted for me and (was) really always in my corner," Hoover said. "It was just devastating to watch how all this has unfolded, and the Billy that I know and a lot of people would say has the biggest heart of anybody and he is a good person."