The 23-year-old woman was waiting at a stop opposite St James’s Hospital in Beckett Street when she was approached by a man.
He produced what appeared to be handgun and demanded her handbag.
He was disturbed when another woman arrived at the bus stop and pointed the gun at her before running off with the victim’s white Motorola Moto 4G phone.
The suspect was described as white, aged 17 to 18 years old, around 5ft 6ins tall and of a skinny build.
He was wearing a green striped woolly hat, baggy light blue jeans and a white or light-coloured bomber jacket with a darker pattern or motif across the chest.
The incident took place at around 7.20pm on Monday, November 9.
Detective constable Darren Young, of Leeds District CID, said: “The victim was understandably shaken by what happened and we are keen to identify this male.
“We would like to hear from anyone who recognises him from the description given.
“There was an elderly Asian man waiting at the bus stop at the time the incident occurred and we are keen to trace him as a witness.”
The robber ran off in the direction of Stoney Rock Lane after the incident.
Anyone with information is asked to contact police at Elland Road via 101 or independent charity Crimestoppers anonymously on 0800 555 111.