It is understood the bus driver had challenged the passenger over his refusal to wear a face covering.
Police released a CCTV image on Thursday of a man they want to speak to in connection with the assault.
London Ambulance Service attended alongside Metropolitan Police officers, and the bus driver was taken to hospital and received treatment.
He has since been discharged and has fully recovered.
Detectives from the Met’s Roads and Transport Policing Command are investigating and have recovered CCTV from the bus.
Passengers have been legally required to wear face masks on public transport for more than a year now.
Even as restrictions eased this week on some public transport networks, Mayor of London Sadiq Khan has mandated that face masks must continue to be worn on Transport for London services, including buses in the capital.
Only those with exemptions for medical or other reasons are able to not wear a face covering on public transport.
Watch: Jacob Rees-Mogg waves face mask in the air but refuses to wear it