This is an excellent question, many books have been written regarding the issue of the Bible’s historical reliability. Some good ones are:

These books will be able to answer your question much more fully than I can ever do so here.

The first thing I would like to point out is that inherent in the question is an assumption that it is important that the Bible is true. No one seems to mind if the latest Harry Potter novel is true or not. This is because the Bible claims to be a true presentation of history. So the gospel according to Luke begins:

‘Many have undertaken to draw up an account of the things that have been fulfilled among us, just as they were handed down to us by those who from the first were eyewitnesses and servants of the word. Therefore, since I myself have carefully investigated everything from the beginning, it seemed good also to me to write an orderly account for you, most excellent Theophilus, so that you may know the certainty of the things you have been taught. In the time of Herod king of Judea there was a priest named Zechariah, who belonged to the priestly division of Abijah; his wife Elizabeth was also a descendant of Aaron.’

Luke is gathering evidence, he is interviewing people to write his account. He is giving his account a historical framework, the time of Herod, king of Judea. Luke is full of little historical tidbits like this. He names governors, priests, landmarks, practices that agree with other historical materials (other histories by the Roman Tacitus and the Jew Josephus, stone inscriptions etc).

We also have a historical chain of documents that refer back to these original documents as being real representations of history. These are documents that date back to the early history of Christianity that quote Biblical texts and refer to to them as historically accurate accounts (have a browse through earlychristianwritings.com).

The bible is also realistic in the sense that it does not read like fiction. There are elements in the Bible, particularly in the gospels, that don’t read well for Christians. That the apostles run away when Jesus is arrested is not what you would expect to read in an historic forgery. Yet this, and others like it, is what we discover as we read the Bible - the leaders are human and make human mistakes.

Outside the bible we also find support for its accuracy. There are other historical references to Jesus and Christianity. I mentioned Tacitus and Josephus before, Tacitus states in his Annals (15.44) 
Consequently, to get rid of the report, Nero fastened the guilt and inflicted the most exquisite tortures on a class hated for their abominations, called Christians by the populace. Christus, from whom the name had its origin, suffered the extreme penalty during the reign of Tiberius at the hands of one of our procurators, Pontius Pilatus, and a most mischievous superstition, thus checked for the moment, again broke out not only in JudÃa, the first source of the evil, but even in Rome, where all things hideous and shameful from every part of the world find their centre and become popular. ‘
Pliny the Younger described the Christians as, amongst other things, worshipping Christ ‘as to a god’. These men had no love of Christians, Pliny was eager to wipe out the Christians in his region of control, and yet their words agree greatly with the Biblical presentation of the historical events. Above Tacitus mentions Pontius Pilate, that Christ died and that it happened in Judea during Tiberius Caesar’s reign.

The Bible has also been accurately transmitted. While the original texts do not exist, ther are numerous, plentiful and remarkably intact parts of the bible that date back to the time the texts were first written. Compared to other ancient documents, the integrity of the text of the Bible is impressive.

So there is great support to viewing the Bible as being historically accurate. However, is it true? Those who wrote the Bible were far from impartial but impartial reports are rare. It is a funny concept in a way. The very act of writing something down seems to suggest some level of partiality towards or against something. Can you imagine sports reports from someone who has no interest in sport? They would be scant at best. The Bible has been written by people who are open about their interest in Jesus. They want you to believe in Jesus as they do. Does this make their accounts untrue? If, as we have seen, the Bible is historically accurate, and if the authors were willing to put their lives on the line for what they believed (and many of them lost their lives) - they were reporting truth.

For me personally, there are two things that commend the truthfulness of the Bible. The first is its explanation for the resurrection of Jesus. Something happened on that Sunday morning and all explanations that disagree with the Bible’s fall flat. The second is that the Bible tells of Jesus, the man who changed the lives of the authors, the lives of many great men, the man who changed the course of history and changed my life as well. After recommending that you read ‘Is the New Testament Reliable?’, I urge you to more importantly read the Bible for yourself. Start at the gospel of Luke and ask yourself if what you’re reading seems true.