Police said the man grabbed the shoulder strap of the 36-year-old woman's handbag but let go after members of the public intervened during then the incident, which happened near Greggs at the bus station just after 9pm on Wednesday. (November 4)
The victim jumped onto a bus and left the area unharmed.
The suspect is described as a 6ft tall slightly overweight white man. He was wearing a checked jumper with a diamond shape pattern and dark coloured long coat. The woman described him as having 'bad skin' and a wide nose. She told police he spoke with a Yorkshire accent and smelled of alcohol.
PC James Taylor of Leeds District Police, said: "We are carrying out enquiries and would like to speak to anyone who may have witnessed this incident which left the victim unhurt but very upset. I am particularly keen to speak to members of the public who intervened and would have had a good look at the suspect."
He added: "We know this male confronted the victim shortly beforehand at the junction of Chapeltown and Church Lane but she was able to get away from him by going into a shop. "Anyone who saw this or has any information which could assist us is asked to contact myself at Leeds District Police on 101 referencing crime number 13150445169.
"Information can also be passed anonymously to the independent Crimestoppers charity on 0800 555 111."