The 17-year-old boarded the 107 bus at Market Street, Haddington, bound for Dunbar, at around 6.30pm on Wednesday.
Once on board, she was sexually assaulted by a male passenger in what police have described as an “very upsetting ordeal”.
The attacker eventually moved to the front on the East Coast Buses service and alighted at Mill Wynd, East Linton, where he walked off in an unknown direction.
Officers are now appealing for information.
The suspect is described as a white man in his early to mid-40s. He has a slim build and is quite muscular with short cropped grey/brown hair.
He was wearing a grey hooded top with loose jeans and was carrying a dark blue bag.
Police Sergeant David Aitchison, of Haddington police station, said: “This was a very upsetting ordeal for the 17-year-old victim and it is important that we trace the man responsible as soon as possible.
“I would urge anyone who was on the number 107 East Coast bus on Wednesday December 14, and remembers this incident, or recognises the suspect description, to get in touch with us immediately.”
People with information are urged to contact police on 101 or Crimestoppers, anonymously, on 0800 555 111.