The attack was reported at 1:50 p.m. Tuesday near De Haro Street and Southern Heights Avenue.
Officers arrived to find the 26-year-old victim still seated on the bus, visibly shaken, according to police.
The victim said she was in her seat when the suspect suddenly punched and kicked her several times, police said.
The bus driver intervened and ordered the suspect off the bus. She loitered in the area for a while but fled before officers arrived, according to police.
The victim told police she heard the suspect make remarks about her race.
A witness corroborated the victim's story, and said that when he asked the suspect why she had attacked the victim, the suspect said it was because of the difference in their races.
The victim refused medical treatment at the scene. Surveillance video from the bus is being used in the investigation of the attack, which is being treated as a hate crime.
Police believe they know the suspect's identity but have not released her name. They are working to obtain a warrant for her arrest.
Anyone with information about the case is encouraged to call the Police Department's Bayview Station at (415) 671-2300, the department's anonymous tip line at (415) 575-4444 or send a tip by text message to TIP411.