The 15-year-old was sitting at the back of the vehicle when she was subjected to the indecent act by a man sitting nearby,
The incident happened on the No 276 First bus as it was approaching Bridgeton Cross last Sunday at around 8.40pm.
The man got off the bus in London Road between Tobago Street and Green Street, and was last seen walking west in the direction of the city centre.
Police said the teenager had been left "distressed" by the incident.
There were other passengers on the bus and detectives have appealed for witnesses to come forward.