Officers are appealing for witnesses or information about the incidents on the number 5 and 12 services.
Police are working to establish whether the cases are linked.
An 18-year-old girl was sexually assaulted by a man who sat next to her on the number 5 bus on Monday, November 26.
The same man had previously made comments that made her uncomfortable and touched her inappropriately, police said.
He is described as dark-skinned, aged 40 to 60, of a larger build, with short or shaved hair wearing a black jacket. He has previously been seen travelling from Huntington Road towards York railway station at around 4pm on either the route 5 or 12 bus.
In a separate incident, a 19-year-old girl was approached by a man twice as she travelled on the number 12 bus from Monkton Road into the city centre.
On the first occasion he touched her hand inappropriately and made inappropriate comment. On the most recent occasion, on Wednesday, November 14, he sat near her and asked her questions that made her uncomfortable.
He is described as black, around 40 years old, of a "fat build" and balding, officers said in their appeal.
Anyone with information is asked to call North Yorkshire Police on 101, select option two, and ask for David Allen (collar number 1759), or email Detective Constable Allen on [email protected]
People can also pass information to Crimestoppers on 0800 555 111.
Quote the North Yorkshire Police reference number 12180220537.