She is described as white, in her mid-30s, around 5ft 7in tall with a heavy build, shoulder-length hair that is dark at the roots and lighter at the ends, and glasses.
At the time of the incident, she was wearing blue jeans and a long grey coat.
Constable Shona MacKay from Leith Police Station said: "The comments directed towards the member of bar staff were completely unacceptable and we continue to progress this inquiry to trace the suspect.
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"We are keen to hear from anyone who recognises the woman pictured in the CCTV footage and would ask the public to come forward if they can help us identify and trace this individual.
"In addition, anyone with any further information relevant to this investigation should also contact police immediately."
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