The Metropolitan Transportation Authority identified the victim as Allen Thomas, 51, an employee of five years.
The alleged shooter was identified by the Los Angeles County Sheriff's Department as 41-year-old Anthony Craig Chambers of Los Angeles.
The relation between the two, if any, was not known, and the motive was unclear. The MTA said the shooting was "highly unusual" and that it's something of great concern to them.
"It's hard to express in words the feelings that we have at this time," said MTA spokesman James Woodson.
Craig allegedly shot Thomas in the torso shortly after 9 a.m. Sunday while riding on the Route 105 bus heading east on Santa Monica Boulevard, west of La Cienega Boulevard in West Hollywood. Investigators said it appears Craig was the only passenger on the bus at the time of the shooting.
After allegedly opening fire on Thomas, Craig was seen jumping out of a bus window and running down the street. Deputies arrested him without incident and he was being held on $1 million bail. Deputies recovered two guns from the bus.
Thomas was rushed to Cedars-Sinai Medical Center, where he later died of his injuries.
Gail Dotson, Thomas' aunt, was left in disbelief. Thomas' murder happened the morning after the family buried his grandmother.
"I got to shaking real bad so I just laid down to rest and calm my nerves down," Dotson said. "I'm going to miss him a whole lot."
Investigators said they hope the security camera on board will shed light on what took place. The MTA has yet to announce if there will be any changes made to safety protocol.
Some MTA drivers said they are concerned about their safety, but they added that it's hard to prepare for circumstances they simply can't predict.
A makeshift memorial of flowers, candles, cards and a picture put together by co-workers grew at the site of the shooting. Hundreds of people attended a candlelight vigil for Thomas on Monday night.
"This is a tragedy for us. For us to do our job, put our lives on the line everyday to pick up people and to have one of us killed, one of our colleagues killed, is a tragedy," said MTA driver Jessica Eiland.
MTA has provided grief counselors for their employees. Thomas leaves behind a wife, mother and an adult son.