The most serious offence happened at around 20:00hrs on Friday, 8 October.
The top floor of the 154 bus from Croydon to Morden was set alight while it was travelling down Mollison Drive, South Beddington.
The driver evacuated the bus after they became aware of the fire, no injuries were reported.
The bus was completely burnt out and the damage is estimated to be in the region of £200,000.
Police also want to speak to the man in connection with an arson on a 154 bus that occurred on Sunday, 3 October.
A small fire was discovered at the rear of a bus that was traveling from West Croydon to Morden.
This fire was extinguished before serious damage occurred.
Officers from the Met’s Roads and Transport Policing Command investigate.
Anyone who recognises this man, or any witnesses or people who have information that could assist the investigation are asked to call police on 101 or contact via Twitter @MetCC. Please quote CAD8509/08OCT
To give information anonymously contact Crimestoppers on 0800 555 111 or online at crimestoppers-uk.org.