A woman was left “extremely distressed” after the incident on the Arriva 127 service between Dewsbury and Wakefield.
The man committed the indecent act sometime between 9.30am and 9.42am on Monday, March 31.
He got off the bus on Dewsbury Road, in Gawthorpe, after he was challenged by the bus driver.
And police have released this image of man they want to speak to in connection with the incident.
Inspector Mark Chamberlain said: “A female passenger has been left extremely upset and distraught by this incident and we are keen to identify the man responsible.”
Anyone with information should call the Ossett neighbourhood police team on 101 or Crimestoppers, anonymously on 0800 555111.