Detectives are appealing for witnesses to come forward.
Det Supt Fiona Van Kampen said: “We recognise the intense concern this will cause within the local community, and are working to establish the exact circumstances of the attack.
“This took place on one of London’s busiest bridges, so we are urgently appealing for anyone with information to come forward.
“If you have dash-cam or mobile phone footage of what happened, it is important that we see it.
“Our thoughts remain with the victim’s family as inquiries continue.”
Siwan Hayward, director of security, policing and enforcement at Transport for London, said: “Our thoughts are with the bus driver, his family and his friends following this shocking incident.
“We strongly condemn all forms of violence and aggression and everyone has the right to work and travel on London’s transport network safely and without fear.”
