Not sure there would be a direct route from that direction to South Bermondsey.
Your best bet might be to jump on at one of the Surrey commuter towns into Waterloo, then one stop on the tube, or train from Waterloo East, to London Bridge. From there, itās a short hop to South Bermondsey.
Simplest is to get to Waterloo.
Then walk across the concourse, up the escalator to Waterloo East rail station.
Then catch the next train to London Bridge rail station, just one stop.
I am starting off for a drink at The George Inn ā 75 Borough High Street, SE1 1NH, an old coaching inn.
As an alternative for food, there is nearby:
Borough Market Kitchen (street food traders) and restaurants. Near London Bridge
"Surrounding the Market, youāll find a complementary blend of restaurants, bars and shops."
https://boroughmarket.org.uk/traders/?trader-day=saturday
Then, Train from London Bridge station to South Bermondsey Railway Station