The suspect was already on the bus when the woman boarded the Route 141 on Turnpike Lane at around 5.40pm on Saturday January 15.
He reportedly harrassed other passengers before he approached the victim and allegedly touched her several times.
Another passenger intervened and the suspect was removed from the bus following the alleged incident, police said.
The Route 141 bus was travelling to London Bridge.
Detectives have released a CCTV image of the man they need to trace.
The man is described as between 35 and 40 years old.
He was wearing a light pink woolly hat with ‘pearls’ on it and a light brown hooded jacket.
Also, the man was carrying a cross body woman’s purse at the time.
Anyone who recognises the man or has any information is urged to contact police via 101 quoting reference CAD 4526/15Jan, or Tweet @MetCC.
Alternatively, to remain anonymous, call Crimestoppers on 0800 555 111.