They started at 6am on the 4th of July when the victim boarded a Route 116 bus on Staines Road and sat on the top deck.
A man who got on at the same stop sat directly behind her and through the space of the seats tried to touch her inappropriately.
The woman leaned away, however the man then leant forward and touched her waist.
He then reached over the seat, grabbed her over the shoulders, hugged her for around 30 seconds and kissed her on her cheek.
The suspect then followed the victim while at Hounslow Bus Station and grabbed her right arm and tried to pull her towards him for a hug.
The woman told him no several times and tried to pull away but was not able to and he proceeded to kiss her on her cheek.
He asked her twice to do it again and the victim declined before suspect then walked away from the woman.
Around 20 minutes after getting off the first bus, the victim got on a Route H37 towards Richmond.
The suspect followed her on and sat next to her.
Not far into the journey he grabbed the victim’s leg before alighting from the bus at Isleworth Bus Station.
The victim remained on the bus and continued her journey.
DC Charlotte Joseph, of 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, assault and grab a young woman who was simply going about her daily business. It is absolutely not acceptable that any woman should have to deal with this type of behaviour and we are working hard to target those who commit such offences.
“I have no doubt this individual will likely attempt to assault other females, he needs to be identified and caught. I would urge anyone who believes they recognise the man in the images to come forward.”
Anyone with information is asked to call police on 101 quoting CAD 2394/08SEP23, or to give information anonymously call Crimestoppers on 0800 555 111.