The incident happened at around 9.25pm in Nethermains Road near Braes View when the single decker bus window was hit by an object and shattered.
Thankfully none of the passengers or the driver were injured, but police are warning that the vandalism could have caused a serious accident.
Inspector Kellett said: “Throwing items at moving vehicles is extremely reckless and dangerous. Given the icy road conditions this incident could easily have caused an accident if the driver had lost control.”
Officers are keen to identify a group of four youths who were seen on the footpath as the bus passed. One of the youths may have been wearing a grey hooded top.
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Anyone with information is asked to contact Police on 101.