The incident occurred near 94th Avenue East and 136th Street East around 3:30 p.m.
Pierce County Det. Ed Troyer said the incident began seven blocks away at 136th and Median, where a silver car was involved in a shooting. The car then fled the scene, and while speeding off, struck the bumper of the school bus.
No one was injured in the crash. Approximately 20 children were aboard the bus at the time.
Police have arrested a 32-year-old man suspected in the incident, and were questioning him.
Investigators originally believed the bus had been struck by gunfire at least once, but later corrected their report.