The incident happened at 11.55am on 21 November on the M2 bus from Bournemouth to Poole on Poole Road outside the Night Owl takeaway opposite Redlands.
During the attack, the offender twisted the victim’s arm and punched him in the head several times causing minor injuries.
Police Constable Kerry Shelley, of Poole police, said: “I am now able to release a CCTV image of a man I wish to speak with as I believe he can help me with my investigation.
“The offender got off the bus at the junction of Bournemouth Road.
“I would urge the man pictured – and anyone who recognises him – to contact me, in confidence, as soon as possible.”
No arrests have been made.
Witnesses and anyone with information should call Dorset Police in confidence on 101 quoting incident number 21:166. Alternatively, call the free and anonymous Crimestoppers line on 0800 555 111 where mobile phone tariffs may apply.