The car passenger was trapped inside the vehicle and had to be freed by Singapore Civil Defence Force officers.
The collision occurred along Yishun Avenue 8 towards Yishun Avenue 7 around 6am, Shin Min Daily News reported on Saturday.
The bus involved in the accident belongs to AZ Bus.
Ms Cynthia Yeo, an operations executive at AZ Bus, told ST that there were no passengers on the bus at that time, and the driver was not injured.
Ms Yeo, 36, added that the bus usually ferries students or office workers.
The police told ST that they were alerted to the accident at 5.58am on Friday.
“The male car driver and his female passenger were both taken unconscious to Khoo Teck Puat Hospital,” he said.
The driver later died in hospital.
SCDF said it rescued a woman who was trapped in the front passenger seat using hydraulic tools.
It dispatched a fire engine, two Red Rhinos and two ambulances after receiving a call at 6.10am.
Police investigations are ongoing.
Related story: Car-lite, Uber-heavy in Singapore
Related story: Lawyers say tougher to claim against private-hire cars