Someone has said that the only "Bible" some people will ever read is the one they see demonstrated in the life of a Christian.
In other words, sometimes the way we live speaks far louder than our words. Your neighbor may deny the Bible but he can't deny that its message has changed your life (if it has). To put it another way, does he see Christ in you? When he looks at you, does he see someone whose life is filled with Christ's Spirit? The Bible says, "The fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, gentleness and self-control" (Galatians 5:22-23).
Many people who say they don't believe the Bible actually have never read it, I have discovered. Perhaps that is true of your neighbor, and the time may come when you can encourage him to discover it for himself. But don't allow yourself to be drawn into fruitless debates; very few people are ever won to Christ by arguing.
Instead, ask God to help you to show Christ's love to your neighbor, and when he asks questions "to give the reason for the hope that you have. But do this with gentleness and respect" (1 Peter 3:15). In addition, pray for him, for only God can convict him of his sin and his need of Christ.