The sections of experimental bus lane will be alongside Trocette Mansions and Bermondsey Square, and north of Tanner Street alongside Maltings Place.
TfL says the trial will run for up to 18 months, with the lane being operational 24 hours a day
The scheme is part of a project to improve bus reliability and journey times in central London. Similar measures are due to be introduced on New Kent Road.
TfL has published an online survey for local residents and businesses to give their views on the scheme.