She received non-life-threatening injuries and is recovering at San Francisco General Hospital.
Witnesses described the suspect as a six-foot tall black male between the ages of 25 and 40 who wore a full beard, a black sweatshirt and a black knit cap and appeared to be homeless, according to police.
Officers said that description matches the traits of the suspect from an attack on an 11-year-old on September 1.
That suspect was never apprehended.
“We will be saturating the area, looking for the perpetrator,” said Sgt. Wilfred Williams, a police spokesman. “With the description we have today, we will hopefully be able to locate the suspect.”
He said police will check to see if the vehicle had a security camera that recorded the attack.
Officers tried to review security footage after the attack in September, only to learn the camera at the back of the bus wasn’t working.
The similarity in the descriptions of the attacks and the two suspects raised fears about the possibility of a single attacker who could strike again in the future.
“I’m extremely concerned,” said District 8 Supervisor Bevan Dufty, who attended a press conference next to the vehicle where the attack occurred. “I think the situation on Muni is so out of control that we really do need to have officers regularly riding the system.”
Police said the suspect was getting ready to depart the bus when he turned around and stabbed the victim, who was seated, talking to a friend. He then got off the vehicle, which stopped at 18th and Church streets when the driver learned what happened.
No words were exchanged before the attack and no motive has been identified, police said.
“The information that we have right now is that they didn’t know each other and didn’t speak at all,” Williams said.
The circumstances were similar when the 11-year-old boy was stabbed on his way home on the 49 Van Ness-Mission in September, Williams said.
Some passengers said the attacks mean they won’t be riding Muni any more until security on city vehicles is improved.
“It will absolutely keep me from riding the bus today,” said Ronnie Weiner, a pedestrian who said she was planning on taking Muni to get home after visiting family in Hayes Valley.
“To see this in broad daylight in what looks like a pretty nice part of town is really frightening” she said. “I’m going to buy new sneakers so I can walk all the way back instead of taking the bus.”