Why do Christians believe the Bible?

We start with a number of basic beliefs. We believe that it is possible to know things truly. That there is order and consequence in the universe. That it is possible to build a rational construct and that these things are so because that's the way God made them. That God not only exists but that he has entered into a relationship with his creation and with man in particular.

We are taught that truth is established in the mouth of two or three witnesses. So here are my two:
As we study the Bible we discover there are some things that are so obvious we call them common sense. The sun rises each morning and sets each evening (not the other way around and the time it is "up" depends on your location on the earth's surface). Then we discover there are conditional statements which can be checked such as Proverbs 22:15 - "Foolishness is bound in the heart of a child; the rod of correction will remove it far from him." The course of our society over the past 40 years indicates the truth of this one. And finally there are statements we need to take on trust - especially those dealing with our final destination. So, my first witness - Bible study and investigation of its claims - demonstrates the Bible is to be trusted.
Next a comparison between the Bible and the religious writings of other religions shows the restraint of the Bible. Unlike those writings, its claims can be tested by history and science. Luke's writings, his Gospel and the Book of the Acts of the Apostles abound in historical detail which can and have been checked. And, in every case where Luke's history can be checked it has been confirmed. Checking the details of the fall of Jerusalem against the prophecies of Jesus in Matthew 24 and Luke 21 demonstrate how accurate were the words of the Christ. And that's before we enter the study of archaeology and how it confirms the Old Testament. My second witness, the study of the external data referred to in the Bible, demonstrates the Bible is to be trusted.
Then, for the Christian, it is possible to know the author. This usually starts as one of those conditional statements which can be investigated. As we search out the truth of the Bible's statements we can sometimes be surprised by the author himself. When that happens we understand the Bible more clearly than we ever did before and, in fact, even wonder why we didn't see it was sin which stopped us from truly knowing God. Then we understand the Bible as a letter written to all men and to us in particular and we believe it. My third witness also attests to the trustworthiness of the Bible.

So, from without and within, the Bible demonstrates it is to be trusted. Why do Christians believe the Bible? Because life and study demonstrate it is to be trusted.