The woman was on the 423 bus towards Norwood when a man boarded and sat next to her.
He made a number of inappropriate comments towards her before touching her thigh.
An investigation was launched after it was reported to the Metropolitan Police the following day.
Officers have now released an image of a man they would like to speak to.
PC Charlotte Joseph, from the Met’s Roads and Transport Policing Command, said: “This was a really frightening and intimidating experience for the victim, which has left her nervous to travel.
“The suspect thought it was fine to harass, and grab a woman who was simply going about her day. It is absolutely not acceptable that any woman should have to deal with this type of behaviour and we are working hard to identify the man responsible.
“We have conducted a number of enquiries since the incident was reported, including looking at CCTV, speaking with witnesses and facial recognition.
“We are now asking for help from members of the public to identify a man we would like to speak to in connection with this incident.
“I would urge anyone who believes they recognise the man in the images to come forward.”
Anyone with information is asked to call 101 quoting CAD 1779/15Sep or Crimestoppers on 0800 555 111.