Something from outside the Bible made the Bible "the Bible."
A JW would probably answer: This Something was God, plain and simple. He probably not only inspired the writers, he also inspired those responsible for choosing the chapters that went in and the ones that were kept out. If you believe in the former it's not such a stretch to believe in the latter, too.
And if that is not enough to satisfy you, I would say: "It still is the next best thing" we today can get as a written basis for our beliefs. Better trust this book which was completed within 300 years after Jesus death, than anything newer (for example the mormon book) or anything less reliable (for example catholic traditions subject to change).
And Mary Jones? So what? God must have had his reasons. I could also ask why did God not let Europeans discover America 1000 years earlier? All this time the Native Americans had to live and die without knowing about Jesus. Seems kind of fruitless to ask these kinds of questions.
Look, I think many rank and file JWs are quite pragmatic. Maybe their leadership is not perfect, maybe their doctrine and it's origins are not perfect. Many would claim they don't have to be. They believe in God, they want to know what is his purpose for us, and how they can serve him. And they don't want to do that alone, but together with fellow believers. Using the bible and what it tells us about about early Christianity seems like a good start. Certainly better and more verifiable than what most - if not all - other Christian groups can offer.