YD1S is the prefix for a D1 model Bantam in a 'Spring (plunger) frame,' hence the 'S'. The number 59657 indicates it comes from the 1951 production year, which means it was made in 1951 but sold in 1952, ergo a 1952 model.
However, the engine number BD3B is a D3 model Bantam engine, which weren't produced until 1954, and 6758 would be from the 1955 production year. In other words someone has put a later engine in the earlier frame. The second 'B' in the engine number indicates the lighting was powered by the battery (as opposed to the standard 'driect' lighting, powered straight from the generator)
I suggest you get BSA Singles Restoration by Roy Bacon, it's a wealth of information and has some great photos to boot.
Also if you can, try and find a genuine BSA or Ptiman's manual rather than rely on Haynes or after-market publications.
Good luck, it'll be a great project I'm sure.
Blue