The 15-year-old girl was pulled to the ground and assaulted during the ordeal in East Kilbride, South Lanarkshire, on Friday night.
Police Scotland said she was travelling home on a No 18 First Bus at around 11.15pm and the man got on a few stops after her.
He then followed her off the bus at the Calderwood Square stop and attacked her near Aikman Place.
The teenager struggled and screamed, alerting her parents, who ran to help her.
The attacker then fled towards the nearby church.
The suspect is described as being between 20 and 40, 5ft 9ins, of stocky build, with ginger hair and black rimmed glasses.
He was wearing a red hoodie, a black t-shirt and blue jeans.
Detective constable Pamela Bannister said: “This abhorrent individual preyed on a teenage girl who had simply been making her way home from seeing friends and it is absolutely vital that we find him.
“I would appeal to anyone who was on the No 18 First Bus or in the area around the time of the incident, and may have seen a man matching the above description, to please get in touch.
“Additional patrols will be in the area to provide reassurance to the local community and anyone with concerns is welcome to approach our officers who will be happy to assist.”
Anyone with information is asked to contact the divisional rape investigation unit on the 101 number.