The offence at the station happened at about 9am on Tuesday, when the victim was approached by a man who asked for money.
After refusing, the offender brandished a knife.
But he left the scene empty-handed after being deterred by a woman who was passing by.
She also stayed with the victim on the bus following the attempted robbery.
North Yorkshire Police have today (Thursday) appealed for witnesses to the offence to come forward.
The man is described as white, 5ft 10ins tall and of slim build.
He was wearing a dark jumper and dark tracksuit bottoms.
Police also want to speak to the woman who helped the victim to assist their investigation.
Anyone with information is asked to contact North Yorkshire Police on 101, quoting reference number NYP-02052018-0381