He is the drummer, main songwriter, and only constant member of the California punk rock group Descendents since its inception.

In late December 1981, he played a few concerts with the hardcore punk band Black Flag because their drummer, Robo was detained in England after a tour there.

After Milo's departure, Bill and the other members of Descendents, Karl Alvarez and Stephen Egerton, recruited singer Dave Smalley of Dag Nasty, moved to Fort Collins, Colorado, and formed ALL.

Stevenson was born in Torrance, California and attended Mira Costa High School, with fellow members of the Descendents.

One of Stevenson's most recent works was the production of Frenzal Rhomb's tenth studio album The Cup of Pestilence, released April 7, 2023.

After the album, singer Milo Aukerman went to college, the band played rarely, so Stevenson joined Black Flag.

The tumor caused Stevenson to lose motivation and eventually made him gain weight, had a blood clot, diabetes and sleep apnea.