The incident happened in Freuchie, Fife, on Monday – and police have appealed for up to seven witnesses to come forward.
Officers are investigating the full circumstances which led to the 81-year old woman being badly hurt.
She was a passenger on the Number 64 Moffat and Williamson service which was travelling was eastbound on Freuchie’s East End around midday on Monday.
A Police Scotland spokesman said the vehicle braked suddenly to avoid a collision.
As a result, the woman fell forward and sustained a serious head injury.
Police and the Scottish Ambulance Service attended. She was taken to the Victoria Hospital, Kirkcaldy, for treatment, where she remains in a critical condition.
Police Sergeant Ewan Pearce of Fife’s Road Policing Unit said: “Sadly this incident resulted in an elderly lady being seriously injured.
“We are eager to establish the full circumstances that occurred beforehand.
“I would ask anyone who was in Freuchie’s East End at lunchtime on Monday, April 8, and saw this incident to please contact police.” He appealed directly to anyone on the bus to get in touch – “particularly seven unidentified passengers who were on the number 64 who have not made contact with us.”
He added: “Your information may be vital to our investigation and I would urge to get in touch.”
Those with information can contact Police Scotland on 101, quoting incident number 1356 of April 8.