Police spokesperson Frederic Papaux of Fribourg canton, or region, said an unspecified "voluntary act" could have caused the fire on Tuesday night in the town of Kerzers, about 25km west of Bern.
Five people were also injured in the fire, which for locals echoed a New Year's Eve fire in the Swiss ski resort of Crans-Montana that killed 41 young people.
Christa Bielmann, representing the Fribourg police, told Swiss broadcaster SRF: "There is information circulating that a person poured flammable liquid over themselves on the bus and that this caused the fire. But this is part of the ongoing investigation and is being clarified."
"It shocks and saddens me that once again people have lost their lives in a serious fire in Switzerland," Swiss President Guy Parmelin wrote on X.
"The circumstances are being investigated. I offer my condolences to the families of those who died in Kerzers. And my thoughts are with the injured and the rescue workers."
There were no indications that this was a terrorist attack, Martial Pugin, head of communications for the Fribourg cantonal police, told broadcaster RTS on Wednesday morning.
The regional transport bus is operated by PostBus, which is affiliated with the national postal service.
"We are deeply moved by this tragic news. Our thoughts are with the victims, the injured, and all their families," PostBus said in a statement on its website.
"After rushing to the scene, rescue teams noted that the vehicle was totally engulfed in flames," the regional government said in a statement.
Ambulance and helicopter teams ferried three people with severe injuries to hospitals, while two others were treated on site, police said.
Papaux said at least six people were killed.
Police said the identification of the victims could take several days.
The burned-out vehicle was removed during the night and traffic returned to normal as of Wednesday morning.
With Reuters and dpa
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