Officers would like to talk to the man as they believe he may have information which could help their inquiry.
The incident happened on the No. 76 service, which runs from Hengrove to Cribbs Causeway.
The bus was travelling from Bristol centre along Gloucester Road at around 4.45pm on Thursday, September 16.
The victim was touched inappropriately for approximately 10 minutes by a man sitting behind her until he got off the bus at Churchway Avenue.
If you recognise the man in the CCTV image, call 101 and provide the call handler with the reference 522121636.
You can also contact the independent charity Crimestoppers 100 per cent anonymously and free on 0800 555 111 or via their Anonymous Online Form.