In Shakespeare: The World as Stage (2007) Bill Bryson sticks to what can be definitively known about William Shakespeare. Because there's so little hard evidence to go on, the book is not so much a biography as a historical study of the times Shakespeare lived in and what we know of the Elizabethan and Jacobean theater scene. Like anything by Bryson, it's engagingly written. I can't imagine an author I'd rather have write the biography of an enigma.
Bryson is delightfully scathing toward all the claims that someone other than Shakespeare wrote his works, pointing out that there's no evidence beyond some people's inability to believe a moderately educated man from a modest background could be capable of great things. Which, when you stop to think about it, is a pretty obnoxious view to hold.