The offender approached the girl and throughout the journey gave her alcohol, cigarettes and money before kissing her.
It happened on the S6 bus from Swindon to Oxford at around 6pm on Thursday, September 19.
Investigating Thames Valley Police officer, PC Chloe Palacio, said: “I am appealing to anyone who recognises the individual in the image as they may have vital information to assist us with our enquiries.
“Additionally we ask anyone with mobile phone, CCTV or dash-cam footage to get in touch with the force in case it has captured something which may assist this investigation.”
Anyone with any information relating to this incident, should please call 101 or report it online, quoting 43240453066.
Alternatively, if you wish to remain anonymous, you can contact the independent charity Crimestoppers on 0800 555 111 or via its website.