I've done my share of academic research on Elizabeth I and would highly recommend David Starkey. He's brilliant. If you want a good bio, start with him.
He's an expert on the Tudors and has made several good documentaries as well.
I'm currently reading a book by him on Henry VIII's early years.
See his wikipedia entry for a list of his books and tv documentaries:
David Starkey - Wikipedia, the free encyclopedia
Alison Weir also has a bio on Elizabeth, check her out as well. Here's her website:
Books by Alison Weir
Also, under Historical Fiction, you'll find
The Lady Elizabeth, I haven't read it myself but knowing the author, I'd say its worth trying.