If you're looking for correspondence between George Bernard Shaw and a relative named Bert Douglas, you won't find them in a personal collection—because no such letters exist in private hands.
Shaw's vast correspondence is held in public archives, primarily:
To view them, consult the archives' catalogs, request access (often by appointment), or search digitized collections online. Many letters are published in scholarly editions like Bernard Shaw: Collected Letters.
If a museum acquired a private collection after a donor's death, it would be cataloged and accessible through that institution's reading room.