The Stagecoach vehicle was carrying passengers when it was hit in Perth.
The window was smashed at about 4pm on Tuesday, February 5, when the bus was making its way along Western Avenue, near Perth Royal Infirmary.
Tayside Police said the bus passengers may have seen those responsible, described as two children aged between five and 12.
Officers are appealing for witnesses.
In a separate incident, Tayside officers are trying to trace two teenagers who smashed a lorry window in Dundee's Lochee Road, injuring the driver.
The 38-year-old behind the wheel of a gritting lorry had a "lucky escape" after the pair shattered his cab window, police said.