If you're okay with it not being a drama, the closest thing that I find similar to that (awesome drama, by the way) is a manga called
"Bungaku Shoujo" (Literature Girl) by Mizuki Nomura. Although it takes place in a high school, Tohko Amano reminds me a lot of Shioriko because she has the same passion for stories and solves mysteries using her knowledge of books and the characters.
Time of Eve Although not set in a bookshop and not dealing with books at all, this anime series has a similar tone to the Biblia drama because you get to untangle the mysterious story of each customer who arrives in the shop. By the time the episode ends, it surprises you with a twist and at the same time leaves you with a warm feeling.
Also, Aizawa Tomoko is the screenwriter for Biblia. She wrote other series as well, mentioned
here. You can take a look at the dramas listed there to see if you find one similar to what you want. I've heard that
Kagi no Kakatta Heya is very similar to this, but it isn't about books at all.
If I had to pick a drama,
The Liar Game would be it. It has the mysteries and the focus isn't on crimes but how the characters think. There's a manga of this too, which I recommend (I liked it better than the drama actually).
Good luck.
