A woman was approached on Queensferry Road by a man wanting to take pictures of her feet.
A woman was followed off a number 41 bus by a fellow passenger who then approached her and asked to take a picture of her feet.
The man had earlier moved to sit next to the woman on the bus, and got up to leave after she did.
The incident happened on Queensferry Road on Friday August 11 around 9:30am.
Police have confirmed that they are carrying out an investigation.
It is understood that the man, believed to be in his forties, also complimented his victim on her feet before asking if he could then take a photograph.
A Police Scotland spokeswoman said: “Police in Edinburgh received a report of a man acting in an inappropriate manner on a Lothian buses vehicle on Queensferry Road.
“The matter was reported to police around 11am on Friday, August 11.
“Enquires are currently ongoing.
“Anyone with information is asked to contact officers at Edinburgh Division’s Public Protection Unit on 101, quoting incident number 1098 of August 11.”
A spokesperson for Lothian said: “Lothian takes the safety and comfort of our staff and customers very seriously.
“Through our dedicated Police Liaison Officer, Lothian works in partnership with Police Scotland to ensure that our customers and staff can travel in a safe environment at all times.
“We will always work closely with Police Scotland in the provision of information to assist in their ongoing investigations and would urge anyone with any information to come forward.”