Bonham was born in the town of Dudley, West Midlands. He 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 U.S. 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.
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 April 28, 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.
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 which 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, 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.
Bonham joined the group Black Country Communion late in 2009 and is currently recording music with rock icons Joe Bonamassa, Glenn Hughes, and Derek Sherinian.In 2010, Bonham formed Jason Bonham's Led Zeppelin Experience, a live homage to his father's band, which toured worldwide through 2011