The incident is said to have occurred on Tuesday 8 September at around 15:30 on the Number 11 route.
The bus was leaving the Town Terminus and heading north towards the Bridge at the time.
Police say there were a number of passengers on board at the time and are asking to speak with anyone who may have witnessed the abuse.
In particular, officers would like to speak to a female with two children.
Anyone with any information is asked to contact PC 204 Mark Shields on 725111, or alternatively contact Crimestoppers anonymously on 0800 555111.
Pictured top: The incident happened on the Number 11 bus, which left the Town Terminus in the direction of the Bridge.