The 31-year-old victim was walking along the bridge close to Tooley Street when an N47 bus hit her just before 2.30am today.
She was taken to hospital by paramedics with serious injuries to her right leg, ankle and foot, a spokesman for City Police said.
Her injuries were later found to be "potentially life-changing", he added.
The road was closed southbound while officers investigated but has since been reopened.
Police today appealed for witnesses to the collision to speak to them after the bus driver failed to stop at the scene.