The offence happened between 10.45pm and 11.25pm, when the culprit sat next to the victim and engaged her in small talk before blocking her in her seat.
He then subjected her to a prolonged and repeated sexual assault.
When he and the victim both left the train at Stirling he continued to touch her inappropriately and followed her through the station - before finally leaving the scene.
The man is white, slim to medium build, with short dark hair, and wore a green jacket and chino trousers.
Officers would like to speak to anyone who witnessed the offence or who knows the identity of the man.
They particularly want to speak to a member of the public who was sitting opposite the victim, and who may hold vital information.
Witnesses can contact BTP by texting 61016 or calling 0800 40 50 40 quoting reference 436 of 21/03/19.
Alternatively, call Crimestoppers anonymously on 0800 555 111.