Frightened passengers were forced to duck for cover after their bus was targeted during a suspected airgun attack.
They told how metal pellets smashed two windows on the top deck of the First bus, next to where young children were sitting.
Both windows were shattered in the incident near Cameron Toll Shopping Centre, but were kept from falling on to passengers because they were held together by vinyl sheeting.
Father-of-four John Need, 41, was on the top deck of the X62 service with his four-year-old son Lucas when the window directly behind him was hit, leaving what he described as a pellet-shaped hole in the reinforced glass.
He said: “Had we been sitting in the other seat, the pellet would have been at Lucas’s head height. It doesn’t bear thinking about.
“A little girl started screaming that she wanted to go down to the lower deck. She was hysterical.”
Mr Need, who had been travelling to Summerhall from Peebles, estimated that there were about 12 people on the top deck, including several young children under five.
He added that he was “100 per cent convinced” the bus had come under fire by airgun-wielding thugs.
Other passengers and the driver all reported hearing two distinct bangs in quick succession.
Police Scotland said: “We are investigating after bus windows were shattered after being struck by an unidentified object.
“The incident happened around 3pm yesterday at the junction of Lady Road and Cameron Toll. Inquiries are ongoing and anyone with information that can assist officers with their investigation is asked to come forward.”
Police said it was possible the incident was linked to reports youths smashed a bus window on Friday in nearby Minto Street.
SNP councillor Mike Bridgman, convener of the police scrutiny committee, said: “I hope the police bring them to book before they do any further damage.”
Bus bosses at First Scotland East said they were working with police to establish exactly what happened.
A spokesman said: “The safety and security of staff and customers is our highest priority. We adopt a zero tolerance approach to any acts of vandalism or antisocial behaviour.
“We are thankful that on this occasion our driver and customers were not injured. We are working with Police Scotland to establish who and what caused the damage to the windows and would urge anyone with any information to come forward.”