What is the difference between Bible and the New Testament?

The Bible contains both the Old and New Testaments, so the New Testament is the part of the Bible dealing with the life and teachings of Christ and His Apostles.
[Sometimes, "the Bible" refers to the Old Testament only, when speaking about the pre-Christian era, because it was actually the whole Bible, not only for Jews, but also for Christians, until the late apparition of the NT writings.]