The 24-year-old man died at the scene of the early morning collision, which happened outside the New Victoria Hospital, in the South Side of Glasgow.
The man, who was behind the wheel of a dark grey Hyundai coupe, appeared to steer the car across the carriageway before hitting the front of the double decker.
The No4 First bus was waiting at traffic lights in Govan's Grange Road, near to the junction with Langside Road.
Passengers watched in horror as the car smashed into the bus.
Emergency services rushed to the scene when they were alerted at around 6.40am yesterday.
A First Bus spokeswoman said the firm had launched a probe into what happened.
She said: "The bus was stationary at traffic lights heading towards the city when a car collided with the front of the bus at speed.
"The car driver was pronounced dead at the scene. Four bus passengers were taken to hospital, together with the bus driver.
"We have launched an investigation and are working with the relevant authorities to establish exactly what happened."
Police Scotland said relatives of the man had been made aware and a report would be submitted to the Procurator Fiscal.
A police spokeswoman said the 27-year-old driver of the bus was not injured but was left "extremely shaken".
No passengers were injured in the collision.
Road policing officers at Govan are appealing for information and witnesses.