The armed man boarded the Metro bus with the driver and two passengers aboard shortly before 1am in South Los Angeles, according to the Los Angeles Police Department.
Officers approached the bus as it slowly rolled away.
A cavalcade of police vehicles followed it as the driver drove at gunpoint for the next hour.
A flashing sign on the front of the bus read: "Emergency. 911 Call Police."
Police deployed spike strips, which punctured one of the tyres.
After travelling more than 11km, the bus eventually came to a stop at a downtown intersection near the city's Arts District and the suspect surrendered, officials said.
TV news footage showed a series of small explosions around the bus stopped in the neighbourhood of lofts and warehouses, then police storming aboard with shields.
The bus driver climbed out of window and ran to safety behind an armoured vehicle while officers moved in.
A man was found inside the bus with gunshot wounds but details about what led up to the shooting were not immediately available.
The victim was taken to a hospital where he was pronounced dead, officials said.
The driver and the second passenger were treated by paramedics at the scene and released.
In a statement, Metro said the bus driver was okay and receiving the support he needs.
Police praised the driver for keeping calm.
"This operator continued to operate the bus in as safe a manner as he could under the circumstances, with the police trailing him for an hour before the spike strips finally took effect," Deputy Chief Donald Graham told reporters.
The killing is the latest in a series of violent incidents, including stabbings and shootings, on buses and trains as Los Angeles seeks to expand the transit system ahead of hosting the Olympics in 2028.
In May, mayor Karen Bass called for increased security on transit routes.
In March, a man who indicated he had a gun hijacked a Metro bus in downtown LA and then grabbed the wheel, causing the bus to collide with several vehicles and crash into a hotel.
