Bonham first began playing drums at the age of four, and appeared with his father in the film The Song Remains the Same, drumming on a scaled-down kit. At 17, he joined his first band, Airrace. In 1985, he joined Virginia Wolf, making two albums and touring the US supporting the Firm.

In 1988, Bonham joined former Led Zeppelin Guitarist Jimmy Page for his Outrider album and tour. In May of the same year, Bonham appeared with the three surviving members of Led Zeppelin for a performance at Atlantic Records 40th Anniversary concert in New York City.

In 1989, Bonham appeared as a special guest at the Moscow Music Peace Festival, performing the song "Rock and Roll" with many major rock stars of the day. That same year, he formed his own band, Bonham, whose Zeppelin-inflected first release The Disregard of Timekeeping had a hit single, "Wait for You" and the music video for the subsequent single "Guilty" did get some play; however, after a lukewarm reception for their 1992 release, Mad Hatter, the band was dissolved, and Bonham concentrated on session work and guest appearances.

On 28 April 1990, Bonham married Jan Charteris, in Stone, Kidderminster. His wedding reception included a jam with Jimmy Page, Robert Plant and John Paul Jones. The Bonhams have two children: a son named Jager and a daughter, Jaz (born 1993).

Bonham drummed for Paul Rodgers on the Grammy nominated Muddy Water Blues: A Tribute to Muddy Waters project. A year later with Slash and Paul Rodgers, he appeared at Woodstock II in 1994. Bonham reformed his band with a new lead vocalist, Marti Frederiksen, replacing Daniel MacMaster. Renamed Motherland, they released the album Peace 4 Me later in 1994; however, his down-to-earth nature always showed—on one occasion making an encore drumming appearance for local Led Zeppelin tribute bands Fred Zeppelin and Led Zepagain.

In 1995, Jason represented his father when Led Zeppelin was inducted into the Rock and Roll Hall of Fame, with his sister Zoe by his side. Bonham soon put together another solo project that culminated in In the Name of My Father - The Zepset, which featured the songs of Led Zeppelin. Proceeds from the album went to charity. The album followed up with When You See the Sun.

Jason Bonham also appeared in the movie Rock Star, 2001. Bonham played Drummer A.C., of the fictional band Steel Dragon. The film also featured performances by Musicians such as Zakk Wylde, Jeff Pilson, Myles Kennedy, Jeff Scott Soto, Brian Vander Ark, Blas Elias and Nick Catanese. He also played on the film's Soundtrack.

Bonham starred with Ted Nugent, Evan Seinfeld (Biohazard), Sebastian Bach (Skid Row), and Scott Ian (Anthrax) on the VH1 reality television show, Supergroup, in May 2006. The Musicians formed a band called Damnocracy (after ditching the names FIST, God War, and Savage Animal) for the show, during which they lived in a mansion in Las Vegas for twelve days and created music. Jason also played drums live with Foreigner from 2004 to 2007 and part of 2007 to 2008.

On 12 September 2007, it was announced that Jason Bonham would step into his father's shoes and play drums for a Led Zeppelin reunion concert. This took place on 10 December 2007 at London's O₂ arena as part of an all-star tribute to Ahmet Ertegün. His performance was described as "flawless" by music critics.

In February 2009, Jason Bonham and James Dylan began working together in what would become Jason Bonham's Led Zeppelin Experience, a live homage to his father's band. In autumn of 2010, Jason Bonham's Led Zeppelin Experience embarked on their first North American tour and toured worldwide during 2011.

Bonham more recently played drums, along with sisters Ann and Nancy Wilson of the group Heart on vocals and guitar respectively, for a performance of Stairway to Heaven during the Led Zeppelin tribute at the Kennedy Center Honors in December 2012 while band members Robert Plant, Jimmy Page and John Paul Jones looked on.

Bonham has produced his own line of signature series drumstick with Pro-Mark. The SD531W is made of American Maple with acorn shaped, wooden tips. The taper is relatively short and the sticks have considerably large dimensions, being 16.75" (42.5 cm) in length and 0.595" (1.5 cm) in diameter. The sticks also feature the symbol used by Bonham's father, John Bonham, of the three interlocking rings – they are printed next to Jason's signature on the side of the stick.

In 2014, Bonham joined Sammy Hagar's supergroup The Circle. The band featured Led Zeppelin tracks along with songs from Hagar's various career projects, such as Montrose, Van Halen, and Chickenfoot.

From early March to late May 2015, Jason Bonham's Led Zeppelin Experience toured extensively North America. On 4 December 2015, the band kicked off their North American Winter Tour in San Jose, California. In early May 2016, they embarked on a one-month / 22-date North American tour.