Officers last night spoke to people in the city's Buchanan Bus Station in a bid to jog their memories of Manvir Singh.
Manvir, 21, from Bishopbriggs, got on the XX24 Stagecoach bus at the station's stance six at around 5.15pm on March 19.
He got off the bus in St Andrews, Fife, shortly after 8pm and was last spotted on CCTV in the Fife town at about 9pm.
From around 4.45pm yesterday, a Police Scotland team handed out posters with a picture of Manvir and asked travellers passing through the station to think back to the date he vanished.
Meanwhile, officers in St Andrews were stopping and speaking to people there. It is hoped that the activity will bring up new lines of inquiries.
Police had first thought Manvir travelled to Man-chester but that turned out to be a false CCTV sighting.
Chief Inspector Rob Hay said: "This is about raising awareness of Manvir's disappearance and getting people to think back.
"This is a commuter route so there may have been people travelling who were on the same bus as Manvir three weeks ago.
"Did you see Manvir on the bus? Did you talk to him either on the bus or at the bus station before he got on? Did you see him get off the bus in St Andrews?"
Mr Hay said they had not established a significant reason for Manvir to have travelled to St Andrews. He said Manvir, who is known as Sonu, had a "limited amount of cash" with him.
Manvir's family - dad Harpal, mum Kirandeep and sister Hartneet - are distraught at his disapp-earance and lack of contact.
Mr Singh said: "If anyone has seen Sonu or knows where he may be, please do get in touch with the police so that we know he is safe and well."
Mrs Singh said: "We just want you to know that you are not in any trouble and that everyone is worried about you."
When Manvir was last seen he was wearing a navy hooded top with yellow markings, dark jeans and dark boots. He was carrying a black bag.