A 70-year-old woman quietly sitting on a Brooklyn bus was shot in the cheek by a bullet meant for a gangbanger Tuesday afternoon, cops and law-enforcement sources told The Post.

The injured lady, Gloria Flores, was left bleeding from the graze wound, which was caused by gunfire outside the bus that went through the back of the vehicle, said sources and the bus’s driver.

“I don’t know what happened — it was a mellow crowd, there was no fighting, no noise, no arguing, just, ‘Bang! Bang! Bang!’ ” the driver, who only gave his first name, Jesus, recalled of the 2:30 p.m. incident on Fulton Street in Bedford-Stuyvesant.

“In between Thompkins Avenue and Brooklyn Avenue, I heard at least three gunshots,” he said.

“I went through the intersection, and I stopped here and opened the doors, and everyone ran.

“I turned around. She slumped forward holding her left hand to the left side of her head,’’ he said of Flores.

“The blood is still here,’’ he said, pointing to the floor.

Cops said the hurt woman was taken to Kings County Hospital in stable condition.

Law-enforcement sources said the intended target was a 29-year-old suspected member of the Richfam gang, who took a bullet to the left leg in the broad-daylight street shooting.

The man has been arrested more than 40 times, including for grand larceny, sources said.

NYPD Chief of Detectives Rodney Harrison said at a press conference later Tuesday that the shooter was “wearing a red or orange jacket with a gray bottom, jeans and white sneakers” as he fired “several rounds right off the corner of Thompkins and Fulton Street.”

The driver Jesus said the victim of the stray bullet was sitting one row behind the back door on the right side of the bus — as he pointed to her bloodied aisle seat and the blood-stained metal handle in front of it.

“This is crazy,’’ Jesus said.

He said there were cameras on the bus that should have caught the shooting.

-Additional reporting by Joe Marino and David Meyer