Vintagebentleys.org is the web-based resource for tracking down your desired vintage Bentley.
I used it often while writing Hunt for the Blower Bentley. And visit it often for pure entertainment.
There you can search every W.O. Bentley by chassis number. Find reference materials. Get information on how to repair your early beast. Or even help others identify their own Bentley mysteries.
All in all, a fantastic enthusiast run site. And the place to start to see if you can do better than I or others in finding out what happened to supercharged Bentley SM 3912.
Another option is the Bentley Driver's club itself. Here you can contact the club historian and get all the info you need. Or want. Or that they have.
Happy car hunting.