Lorraine Kirkwood, 37, was last seen with a man as they got on to a bus in the East Dunbartonshire town.
Police had appealed for other passengers to contact them.

Dr Margaret Ann Rous, who was 37, and her 28-year-old husband David Rous were killed when a light aircraft struck the ground in Glen Etive.
The couple, from Newport-on-Tay in Fife, had been flying from Dundee to visit relatives on Tiree.
The emergency services had been alerted when contact was lost with the Piper Cherokee at about 13:50 on Saturday.
Police Scotland said the wreckage was discovered on the northern aspect of Glen Kinglass at 20:00, along with the remains of the two people on board.
Dr Rous' sister Johann Maclean paid tribute to her on social media.
She posted on Facebook: "Today has been the hardest day of my life, I love you Minnie xxxx"
She also thanked friends and family for their sympathy messages.
"Thank you all for the heartfelt messages, phone calls and visits," she wrote. "We appreciate your thoughts at this heartbreaking time xx."
Following the discovery of the wreckage, specialist officers remained at the scene in the Beinn nan Lus area of Glen Kinglass.
Inquiries are continuing into the cause of the accident.

Durant, 28, limped out of Tuesday's game after team-mate Zaza Pachulia fell on his left leg and caused a sprained medial ligament and leg bruising.
It is hoped he could return before the end of the regular season on 12 April.
The 2014 NBA Most Valuable Player joined the Warriors this season in a deal worth a reported $54.3m (£43.9m).
Durant had spent the previous eight seasons at Oklahoma City Thunder, where he was a four-time NBA scoring champion.
Western Conference leaders Warriors went into the game with a league-best 50-9 record and have already booked their place in the play-offs.

The model, called Look At All of Me, has been designed by Frances Duffy, a clinical psychologist in the Northern Health Trust.
It aims to equip care home staff with information so they can understand and assess behaviour, particularly when it is most challenging.
Dr Duffy said the new model can meet a patient's specific needs.
"What is so important is that we remember that the patient is still a person and we look at the person's entire behaviour and not just as someone who has been labelled with dementia," she said.
The tool is quite simple - by using initials including A, S, I and P, it records at what time of the day a person is aggressive, sleeping, incontinent or pacing.
Dr Duffy said challenging behaviour is not an inevitable symptom of dementia but often a sign of stress, anxiety and frustration.
She explained how the model worked using the chart of a woman called Elizabeth, who has been diagnosed with dementia.
"The As show when she has been seen as being aggressive," Dr Duffy said.
"That happened every morning between 8am and 9am during personal care. That means she became agitated when people came in to undress and wash her.
"Can you imagine how you would feel if someone that you don't know very well came into your room, perhaps rushed and not very friendly, and started to undress you?
"Of course, you would feel agitated and may come across as aggressive."
She added: "The chart also reveals that every day, between 3pm and 4pm, Elizabeth paces.
"Staff noted that seemed to happen during visiting time when there are lots of strangers in the care home, which can be off-putting and even stressful."
The message is that people with dementia continue to behave and react to situations around them just like anyone else. Just because they have dementia does not mean they will react differently.
Dr Duffy said that the chart allows staff and families to understand a dementia patient's actions and reactions.
"Of course, it is very difficult but when we understand what might be causing the challenging behaviour - which may look like aggression - we can make changes to how that person's care is being delivered," she said.
The model, developed by the Northern Health and Social Care Trust, is being implemented by Avon & Wiltshire and Devon Health Authorities in England.
While the scheme has been rolled out across independent residential care homes in the Northern Trust, the aim is for all health trusts to benefit.
A Kirkintilloch woman reported missing, after last being seen on Saturday night, has been found safe and well.
[NEXT_CONCEPT]
Tribute has been paid to a Dundee GP and her engineer husband who died in a plane crash in Argyll.
[NEXT_CONCEPT]
Golden State Warriors' top scorer Kevin Durant will be out "indefinitely" after injuring his knee in his side's 112-108 loss at Washington Wizards.
[NEXT_CONCEPT]
A new assessment tool has been developed to help evaluate people diagnosed with dementia.