Reddit mentions of A History of the Bible: The Story of the World's Most Influential Book

Sure thing!

If you want something accessible on a college level that I have used in my courses, I'd recommend The Hebrew Bible for Beginners by Lohr and Kaminsky.

Another magnificent but weightier text that touches directly on source critical issues and the history of scholarly theories is James Kugel's How to Read the Bible: A Guide to Scripture Then and Now.

Those are both broad surveys for beginners. On the more narrow question of dating and good for someone with a bit of Hebrew background, an important new-ish book is How Old is the Hebrew Bible: A Linguistic, Textual, and Historical Study by Ron Hendel and Jan Joosten. They do a great job of summarizing the current state of the question. It's the closest thing I have to offer as a consensus or mainstream view.

For a more "minimalist" or skeptical view that focuses on the historical origins of biblical narratives, I would recommend beginners take a look at The Bible Unearthed: Archaeology's New Vision of Ancient Israel and the Origin of Its Sacred Texts by Neil Asher Silberman and Israel Finkelstein.

Later this summer, I am really interested to see John Barton's forthcoming book A History of the Bible: The Story of the World's Most Influential Book. I haven't seen it, but he's great and it seems like a serious piece of scholarship.

I've been reading "A History of the Bible" by James Barton. He's an Anglican priest who taught at the University of Oxford. He lays out the historical-critical approach to understanding the books of the Bible and the Bible as a whole.
I think it's a great read. It does assume that you are already familiar with the stories of the Bible and how the Bible lays out ANE history.