The man was sitting on the top deck of the SL7 bus from Heathrow to Croydon between 8:15 and 9am on Wednesday the 31st of July.
Details of the incident have only just been released.
He is described as around 50 years old with a long, grey beard and was wearing a white t-shirt with a blue turban.
This incident is linked to another one where a woman was allegedly assaulted by the same man in Southall.
This time, the man was described as wearing an orange turban.
Anyone with information should contact police on 101.
