Officers say the incident happened on a Megabus that was travelling from London to Newcastle on the evening of Thursday, December 7.
The bus left Victoria Coach Station in London at 10.30pm before arriving at St Andrews Bus Station in Edinburgh around 7am the next day.
However, the incident in question is believed to have happened shortly before a stop in Newcastle at around 4.30am.
An Asian male sat next to a 31-year-old woman and allegedly touched her inappropriately and tried to kiss her. She rejected his advances.
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The man then moved seats as the bus pulled into Newcastle before they both departed the bus in Edinburgh.
Enquiries into the incident are ongoing and police are now appealing for other passengers on the bus who saw the man to get in touch.
He is described as Asian, of stocky build, taller than 5ft4in, dark eyes and short dark hair. He was wearing a blue jumper with a collared shirt underneath, a jacket on top and dark trousers.
If you were on the bus and saw the man then contact Northumbria Police on 101 quoting log 764 08/12/18 or by emailing the OIC on [email protected]