The coach, which was carrying a cheerleading team from Kent, collided with an Audi car near Flitwick at 06:45 GMT.
Two men from Buckinghamshire and a third from the London area, all of whom were in the car, died.
A fourth man, who was also in the car, has been taken to Oxford's John Radcliffe Hospital.
No-one on the coach was injured.
Bedfordshire Police said the double-decker coach collided with the Audi while it was stationary on the hard shoulder.
"The coach driver was arrested in connection with the incident and taken to Luton Police Station where he is being interviewed," a police spokesman said.
It is understood the cheerleading team are from a university in Kent and were on their way to a sporting event in Birmingham when the crash happened.
Tim Lambkin, director of Sheerness-based Travelmasters, said the cheerleaders were transferred to another vehicle and continued on their way after the collision.
Mr Lambkin said: "It is too soon to comment on the causes of what happened - we have to let the police experts do their work.
"Our hearts and thoughts go out to the families of those who died and the man hurt.
"In the 31 years I've been involved in the company I've never known anything like this."
Police have urged any witnesses to the accident to come forward.
A coach driver involved in a crash which left three people dead on the M1 in Bedfordshire has been arrested.