"They told me if I stopped, the guys in the car would shoot them and shoot me too," Dharmapala said.
"I was really scared, what was I supposed to do? I didn't know what to do so I kept driving."
However, Auckland Transport said in a statement CCTV footage had been removed following the incident and there was no direct threat to the driver.
"NZ Bus managers have viewed footage from the bus and while the two men were agitated there was no direct threat to the driver and he was not kidnapped," AT said.
"Correct safety procedures were followed, he called staff at the depot and they immediately contacted the police.
"He drove the bus to the city depot and the bus was met there by the police and two people were taken away."
Dharmapala believed he would be shot if he stopped the bus and pressed the panic alarm button in the bus an alerted the bus depot of the situation through the radio.
Stuff reports he ran five red lights throughout Auckland city and drove on the wrong side of the road several times to avoid stopping the bus.
Meanwhile, a police spokesperson said one of the men was acting in a paranoid and erratic manner, appearing to be under the influence of drugs when they arrived.
"He had reportedly been making several comments to members of the public," they said.
"Police arrested him at the scene and assisted him in obtaining a medical assessment. The second person was taken into Police care until he was sober.
A 27-year-old man has been charged with multiple offences, including possession of cannabis and resisting police.
The man is due to appear in the Auckland District Court on Wednesday, July 3.