Police in Calderdale are appealing for witnesses to an incident on the number 590 bus.
The bus left Halifax at 5.45pm on Tuesday, December 3, and was heading to Rochdale.
A man got on the bus at George Street and is then alleged to have shouted at passengers as well as being abusive towards them.
It is alleged that he was particularly abusive towards a woman and her young son and that he also abused the driver.
PC Fiona Igo of the Upper Valley Neighbourhood Policing Team, said: “We are appealing for anyone who witnessed the incident that happened on the downstairs of the bus.
“A man we want to trace in connection with the incident is described as aged 45 to 50, of stocky build and with a bald head. He got off the bus on Tuel Lane, Sowerby Bridge.”
She can be contacted on 101 or firstname.lastname@example.org