Police say the suspect is Naisha Moena Bowser, 21, of Durham.
She is not in custody at this time. Bowser is charged with attempted first-degree murder, assault on a public transit operator and injury to property.
Police said the incident happened around 5:30 p.m. March 15 when a female passenger became angry and threw a soda bottle through a windshield, according to witnesses.
Witnesses said she started to argue with the bus driver and a male passenger attempted to intervene.
The female slashed the male passenger's neck with a box cutter, according to the witnesses, and then got off the bus.
Anyone with information on Bowser's whereabouts is asked to call Investigator Junker at (919) 560-4935, ext. 29416 or CrimeStoppers at (919) 683-1200. CrimeStoppers pays cash rewards for information leading to arrests in felony cases and callers never have to identify themselves.