Bush attended middle school at St. Bernard’s School in Manhattan and high school at St. George’s School in Middletown, Rhode Island. He graduated with a Bachelor of Arts in international studies and government from Colby College in 1994. He was also a four-year letterman and a two-time co-captain as a junior and senior with the Mules’ men’s lacrosse team. As of 2017, he is 4th (182), 8th (97), and 4th (85) in career points, goals and assists respectively in program history and was a first-team All-NESCAC in 1994.

Bush began his career hosting the afternoon drive show on WLKZ-FM in Wolfeboro, New Hampshire, later moving to Washington, D.C., where he hosted the midday show on WARW-FM. In March 1997, Bush joined WWZZ-FM (Z104) in D.C. as host of Billy Bush and the Bush League Morning Show, which aired until January 2001.

He married Sydney Davis in April 1998 and the couple have three daughters. On September 19, 2016, the couple announced they were separating. On July 15, 2018, Bush and his wife announced their divorce due to irreconcilable differences.

Bush joined Access Hollywood, a daily entertainment news magazine, as East Coast correspondent in December 2001. He was promoted to co-anchor in June 2004.

In January 2003, Bush hosted a short-lived NBC prime-time version of Let’s Make a Deal. He was also a correspondent for WNBC-TV’s Today in New York morning show.

Bush co-hosted the Miss Universe pageant four times: in 2003 and 2004 with Daisy Fuentes; in 2005 with fellow Access Hollywood co-anchor Nancy O’Dell; and in 2009 with Claudia Jordan. He has also co-hosted the Miss USA pageant four times, with almost the same partners: in 2003 with Fuentes; 2004 and 2005 with O’Dell; and again in 2009, this time with Nadine Velazquez. After the 65th Annual Golden Globe Awards of 2008 were cancelled as a result of the 2007–08 Writers Guild of America strike, Bush co-hosted the 65th Annual Golden Globe Awards Announcement press conference with O’Dell on January 13, 2008.

Bush was named one of Esquire magazine’s “10 Men” in July 2005. “He’s a furious, inventive interviewer, unafraid of playing the fool in exchange for a true reaction”, opined the writer of the accompanying magazine profile.

Bush was a reporter for NBC at the 2004 Summer Olympics in Athens, and was the host for Access Hollywood’s coverage of the 2006 Winter Olympics in Torino as well as the 2008 Summer Olympics in Beijing. In addition, Bush hosted the reality competition Grease: You’re the One that I Want! on NBC in 2007, and stood in for Meredith Vieira for a week of Who Wants to Be a Millionaire shows on April 21–25, 2008. He and Vieira both had credited cameos as hosts of fictional game shows in the 2004 remake of Ira Levin’s 1972 satirical thriller The Stepford Wives.

Bush played the drill sergeant in the 2010 film Furry Vengeance and had a small role as the voice of a newscaster in the 2014 Disney animated film Big Hero 6. He has also had several appearances on television shows including 30 Rock and Donny!.

In May 2016, Bush was selected to be the co-host of the third hour of NBC’s Today. He served as a replacement for Willie Geist.

On October 7, 2016, The Washington Post reported that video footage was released of Donald Trump having a lewd conversation with Bush, with Trump either unaware or unconcerned that his microphone was active. Bush is heard laughing about Trump’s failed effort to seduce a married woman, and joining in by commenting on actress Arianne Zucker’s appearance, calling her “hot as shit.” The video was made on the NBC Studios lot in the course of videotaping an Access Hollywood episode in mid-September 2005, promoting Trump’s cameo appearance in an episode of daytime soap opera Days of Our Lives to promote The Apprentice.

However, Bush received criticism online and calls for his resignation from the show, with The Washington Post stating, “Bush’s public image was damaged—perhaps beyond repair.” He issued an apology, stating: “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 was 33 years old at the time the video was made. On October 9, 2016, NBC announced that Bush was suspended from Today for his role in the 2005 video. He was suspended pending an internal review. By October 17, Bush had been fired.

On May 8, 2019, Telepictures announced they would hire Bush to be the host of Extra. Bush replaced Mario Lopez at the start of the 26th season on September 9, 2019, in a revamp of the show, which was originally to be renamed ExtraExtra.