She has been taken to hospital following the accident, involving a First Bus, just after midday at the junction of Kirkgate and Vicar Lane.
Police say the woman, who is from Leeds, was "conscious and breathing" when she was taken to Leeds General Infirmary.
She has suffered injuries, including a fractured right shoulder, a collapsed lung and fractured ribs on her right side.
Inspector Carlton Young, from West Yorkshire Police said: "The injuries are not believed to be life-threatening but they are having some further X-rays and scans done in hospital."
Part of Vicar Lane was closed for the bus to be moved, with diversions put in place, but it was reopened just before 2pm.