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.

The killing of some 8,000 Muslim men and boys in July 1995 by Bosnian Serb troops was the worst massacre in Europe since World War Two.
A service to bury 136 newly-identified victims will take place on Saturday, 20 years to the day since the massacre began.
Another 6,241 victims have already been identified.
A truck carrying the newly-identified remains left a mortuary in Visoko, near Sarajevo, early on Thursday.
Relatives of the victims cried as coffins were put on board.
Among them was Hafiza Tihic, 60, whose father Ramiz was among the victims.
"I don't know how he was killed, but I remember the moment when he was separated from us," she told AFP.
"I entered a bus and he was put to one side. What did they do to him later? Only they would know," she said, referring to Bosnian Serb forces.
Crowds also lined the streets of Sarajevo as the coffins passed through the Bosnian capital.
On Wednesday, Russia - an ally of Serbia - vetoed a draft UN resolution that described the killing as a "genocide".
Russia's UN Ambassador Vitaly Churkin said adopting it "would be counter-productive, would lead to greater tension in the region".
A coach driver involved in a crash which left three people dead on the M1 in Bedfordshire has been arrested.
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The bodies of dozens of victims of the Srebrenica massacre are being taken back to the Bosnian town for burial.