The suspect allegedly stabbed the victim in the throat in an apparently unprovoked attack while the two road Line 260 around 7:20 p.m.
"The suspect ... appears to have boarded at the same time as the victim shortly before the incident," a sheriff's department statement said.
"The victim stated that the suspect got up from his seat, and (the victim) thought (the suspect) was exiting the bus," the sheriff's statement said. "Instead, the suspect, unprovoked, stabbed the victim in the throat with a knife or other sharp object, and then ran off the bus."
The victim was taken to a hospital in serious condition but is expected to survive.
The suspect was described as a 30-year-old Hispanic man, standing around six feet tall, weighing about 200 pounds with short dark hair and a goatee.
Anyone with information regarding the suspect was urged to contact sheriff's Detective Kyle Ynclan or Detective Sgt. Eric Jaime at (323) 563-5000.
CNS contributed to this report.