Officers said the bus, which was carrying Shepard Magnet Middle students, was struck by a stray bullet on North Hardee Street near Cheek Road.
Fifteen students were on the bus at the time. They returned to school Tuesday.
The bus driver was hit in the head by flying glass. She was treated at the hospital and released.
Police have released surveillance photos of the people they are trying to identify and locate.
NEW: Help @DurhamPoliceNC find these two people. Police believe they have information about a shooting that injured a school bus driver off Cheek Road at Hardee Street. 19 children were on board the 🚌 #ABC11 pic.twitter.com/weS8Z925il— Tim Pulliam (@TimABC11) January 22, 2019
In the meantime, the students who were on the bus received support from the school Tuesday.
"When they came off the bus this morning they were given some time with counselors," Chip Sudderth with Durham Public Schools told ABC11. "They also sat in a restorative circle with each to share their feelings."
Anyone with information is asked to call Investigator J. Harris at (919) 560-4281, ext. 29120 or CrimeStoppers at (919) 683-1200.