Mahmood Essa, 29, touched the 41-year-old on the legs as she sat with her eyes closed after staring at her as he passed her with his confectionary trolley.
The railway employee then licked his lips “in a suggestive manner” and winked at a colleague.
Essa, now of Bolton, Greater Manchester, denied the offences which happened on June 17, 2014 on a train to Glasgow Central station from Manchester Airport, but was convicted after trial by sheriff Valerie Johnston.
The 41-year-old victim, who cannot be named for legal reasons, told Glasgow Sheriff Court she was travelling to Glasgow for a work meeting.
She saw Essa when she was on the train and said “no thank you” when he asked if she wanted anything from the trolley.
But he passed her again shortly after, and stopped at her seat with his trolley and smiled before walking by again.
Essa then tried to join a conversation the woman had with a man sitting at the same table as her.
Procurator fiscal depute Scot Dignon asked: “The behaviour where he parked the trolley and stared, how many times did that happen?”
She replied: “Twice.”
Mr Dignon asked the victim if she requested Essa not to stare and she told him she “felt vulnerable”.
The court was told the man at her table got off and she was then sitting alone.
When she saw Essa coming towards her seat again she pretended to be asleep, with her feet on the chairs opposite her.
In evidence she said: “I felt someone sitting down on the chair, I thought to myself, ‘oh no’, then the guy said ‘Are you having a nice sleep?’, something like that.”
Asked if she opened her eyes she said: “No, because I was nervous.”
She told the court: “He started feeling my leg up with his hand.”
The woman said he went to her knee and she jumped up and shouted “What are you doing?” and he panicked.
Mr Dignon asked: “How did it make you feel?”
She answered: “Sick, vulnerable, because you trust people on the train to be able to travel in safety, not have a worker do that, make you feel like that the whole trip.”
When the train stopped at Glasgow she got off, having been unable to find a member of staff to complain to, and hid in a restaurant in the station to get away from him.
The matter was then reported.
During the same train journey Essa knocked on the door of the back cabin where a female colleague of his was working - an area he wasn’t allowed in.
The 38-year-old woman said he stood in the doorway and licked his lips “in a suggestive manner” then winked.
He mumbled something about paperwork and claimed he had permission to go into the cabin she was in.
She told him she couldn’t help him and closed the door.
Mr Dignon asked how he felt and she said: “Scared and confused. I didn’t really understand, I didn’t like the connotations I have understood it to mean.”
The female was asked what she meant by “suggestive” she replied: “It suggested he wanted to come to the back cabin for something sexual.”
After she closed the door she was too scared to go to the toilet until the train arrived at Glasgow.
The matter was later also reported when the train arrived at its destination.
Essa was put on the Sex Offenders’ register and will be sentenced next month.