In Bangkok, English bookstores are easy to find. Some of them are bookstore chains, while some of them are independent shops. The bookstore chains usually sell new English language books and usually are located in the upscale shopping malls, while most of the independent book shops sell used or second-hand books and are not located in the malls.
The big and well-known English bookstores that sell new English books are Kinokuniya, Asia Books, and B2S.
Kinokuniya is a Japanese bookstore chain that sells English, Thai, Japanese, Chinese, German, French, and so on books. I believe it is the biggest bookstore chain in Thailand. You can see a photo and review of this bookstore here.
Asia Books is a bookstore chain in Thailand that sells English and Thai books. You might find this bookstore chain under Bookazine brand.
B2S is a Thai bookstore chain that does not sell only books, but also quality stationery, CDs, and DVDs. Most of the books in the B2S store are Thai books. They have quite limited choice for foreign books, but if you are finding the popular one, you should find it in the foreign books area in the store. You can see a photo and review of this bookstore here.
If you want to buy new English books, I do recommend you to go to Siam Paragon and CentralWorld. The large branches of the bookstores are at these two big shopping malls. You have more chance to find the book you want.
The used English bookstores that are famous for local and also foreigners who are living in Bangkok are Dasa, Sun books, and book shops at Chatuchak weekend market.
Dasa book café is an independent English bookstore that is well-known for locals who read English books, and foreigners who are living in Bangkok. Most of the books in the store are English, but you can also find other language books such as Scandinavian, German, French and Russian books too. You can see a photo and review of this bookstore here.
Sun books (or Elite used books) is an independent bookstore that sells Japanese and English books. Majority of the books here is Japanese; about one third of the books are English. You can see a photo and review of this bookstore here.
Chatuchak weekend market
Chatuchak weekend market is the biggest outdoor market in Thailand. You can find almost everything you want here, including English books! Since it is a very big market and is always hot, I recommend you to go there by MRT subway and get off at Kampheng Phet station. It will lead you to the middle of the market and many book stalls are waiting you there!
Hope this information helps