A young French woman was killed after she failed to get off the bus at the right stop, police believe.
Amelie Delagrange lived and worked in Twickenham
Amelie Delagrange, 22, was found with head injuries on Thursday night, less than an hour after she was last seen.
Police believe she met her murderer as she cut across Twickenham Green in south west London, to get home.
It follows three other similar attacks on women in the area in the last 18 months and police are investigating possible links between the incidents.
Police said Ms Delagrange boarded the 267 bus but did not get off at her stop.
RECENT ATTACKS IN THE AREA
1: 8 January 2003, 17-year-old girl attacked
2: 4 February 2003, Marsha McDonnell, 19, killed
3: 18 April 2004, 34-year-old woman attacked
4: 19 August 2004, Amelie Delagrange, 22, killed
She was seen getting off at Fulwell Bus Garage at 2153BST, half an hour before her body was found by a passer-by near the cricket pitch on the green.
Her handbag and Sony Ericsson T300 mobile phone are missing and police say their recovery is "immensely important".
They have not ruled out links to the murder of Marsha McDonnell in nearby Hampton in February 2003. She was bludgeoned to death near her home in an apparently motiveless attack after getting off a bus.
A month earlier a 17-year-old girl survived serious head injuries from an attack in nearby Strawberry Hill.
No-one was charged although a 16-year-old boy was arrested in March 2003 in connection with those two attacks and is still being detained under the Mental Health Act.
On Friday police revealed a 34-year-old woman was found with serious head injuries near Twickenham Green after a night out in April.
Although no property was stolen in the other attacks, Det Ch Supt Andy Murphy said that did not mean they were dismissing the possibility Thursday's murder could be linked.
Detectives have issued this picture of Amelie's bag, which is missing
"It's clearly a main line of investigation for us and officers from the Marsha McDonnell murder inquiry and the attack in April are working with us on this investigation."
But he added it was still to early to say Ms Delagrange's death was linked, carried out by a copycat killer, or unrelated to the earlier attacks.
Extra police patrols are being put on in the Twickenham area and Det Ch Supt Murphy said CCTV cameras were being "deployed" and other steps taken to re-assure locals.
And he urged people to be "aware of who is around you" and avoid darkened areas and open spaces when out alone.
Ms Delagrange, who lived and worked in Twickenham, had been in Crystalz wine bar on London Road, in Twickenham, on Thursday.
Police want anyone who saw Ms Delagrange, who had shoulder-length blonde hair and was wearing a red top and white trousers, get on or off the bus to contact them.
Her family is expected to fly over from France over the next few days.