But that's not why we should believe the Bible.
The Bible is a reliable collection of historical documents written by eye witnesses to supernatural events that occurred in accordance with specific prophecies demonstrating the Bible's divine origin.This sentence can constitute an answer to "why should I believe the Bible." The key points of this sentence can then be expanded as necessary for argumentation or explanation. Again, whole books have been written on this subject, but this is a thumbnail argument.
(Bold is for subject headings. Normal text gives the thumbnail of the argument. Italics give explanatory comments that you can go into if time allows and if necessary.)
The Bible is a reliable collection of historical documents ...
We have ample evidence that we have, within a reasonable degree of certainty, what the Biblical authors wrote.
It is frequently claimed that modern Bibles are based on translations of translations that take us far away from the original writings of the Bible. That is false. We have thousands of copies of the Biblical texts in the original languages. We also have thousands of early translations. We also have quotations from the Bible in the writings of saints of the past. With all of these sources, we can determine what the original text really said.
We also have ample evidence that the authors wanted to and were able to honestly record what happened.
The authors tell us they wrote what they heard and saw or what they carefully researched. They share embarrassing or confusing things they could easily have left out. Where they can be checked against archeology, they have held up.
...written by eye witnesses to supernatural events...
These people wrote about what they saw, and what they saw were things that couldn't have happened by natural means. From a handful of men routing armies to the raising of the dead, the authors recorded a series of impossible things.
...that occurred in accordance with specific prophecies demonstrating the Bible's divine origin.
Those impossible things were, in many cases, foretold. Prophecies come true throughout the Bible — for example, the destruction of Tyre or Cyrus' returning the Jews to Israel — but most center around Jesus. There are more than a dozen very specific prophecies fulfilled in the life, death, and resurrection of Jesus. Those prophecies and the supernatural events they foretold are the proof that the Bible was not written merely by men. God is the ultimate author of this book.
This argument is the strongest for the New Testament. If we have to further bolster the case for the Old Testament, I argue that the support of a man who died and rose from the grave gives it more than enough credibility.
The above borrows heavily from The Ever-Loving Truth by Voddie Baucham and The Case for Christ by Lee Strobel.