The bet is frankly successful, his book is not only rewarding but also fun to read and full of stunning small or funny finds.
That said, the reader should know in advance three things:
this book does not greatly deepens discussed theories. It explains a little, with a lot of teaching but is not an equivalent of a Brief History of Time Hawking, level complexity. What will be a plus for a novice audience in the matter (without that this should push people a little more aware but want a history of science readable). Bryson also happens well to show how, while having progressed incredibly in our understanding of the universe and of life, we still do not know much about stuff.
Bill Bryson tells great scientific advances, including the theories (now) fanciful previous centuries, mixing the history of these discoveries than their discoverer (the book is peppered with anecdotes about the unmanageable temperament or distracted like and such scientific and also speaks often forgotten by the history of science). Without being a novel, the book is far from a daunting list arid facts. I also noted a passage where Bryson racing and passes an urban legend (no, NASA has not lost the data of Saturn and Apollo program -they are very well stockées-: it's just that the ancient plants manufacturing parts for these machines no longer exist). There may be other nonsense but any book peppered with anecdotes like this one finally said in some of them and I do not mind reading.
Only downside I found: the author wrote it in 2003 and the "age" of the work can feel slightly when Bryson tackles the most recent theories, some of which have already been scanned (or at least partially discounts involved) in twelve years. This does not affect what Bryson has written but just want to give a revised edition.