Officers are investigating four reported offences across the two boroughs, one involving a girl aged 15, which they believe to be linked.
The third occurred on Saturday May 9, at around 11.20am, on a route 116 bus between Bedfont Green and Hounslow, and involved a 15-year-old girl.
The fourth offence was on Monday May 11, at around 10.45am, this time involving a 35-year-old woman who was on a 192 bus travelling to Hayes.
Police want to speak to the man pictured.
He is described as an Asian man, aged 40-55, 5ft 3ins to 5ft 9ins tall, and with dark brown/black hair and a moustache.
Anyone with information is asked to call DC Emma Jones, of the Met's Roads and Transport Policing Command, on 020 3054 6181, or Crimestoppers, anonymously, on 0800 555 111.