I, as a Christian, believe everything in The Bible. Then I meet a man who claims himself to be Jesus Christ. Can I immediately disbelieve that man based on some arguments from The Bible?
If you are referring to Christ's second coming:
Your story implies that Jesus has come in some sort of secret way. Consider the implications of
1 Thessalonians 4:16:
For the Lord himself will come down from heaven, with a loud command, with the voice of the archangel and with the trumpet call of God, and the dead in Christ will rise first. (NIV)
When Christ's overt return is upon us, it will be apparent. If you didn't notice Him coming down from the heavens, if you didn't hear the trumpet call and the voice of the archangel, if you didn't see the dead in Christ rise, then it's very likely you are not talking to the risen Christ in His magnificent glory.
Also, Christ warned us himself that many false prophets and false messiahs will come (Matthew 24:4, 11 and Luke 21:8). At that point, you might find it useful to learn how the Bible teaches us to test the prophets.
If you are referring to Christ's first coming:
If you are fully convinced that Christ has already come in the 1st century, then any prospective Christ would first need to convince you that Jesus was not the Christ. Convincing you of that is a highly personal thing. What would it take to convince you that Jesus was not the Christ? Then, if you got to that point, this new prospective Christ would have to fulfill the Old Testament prophecies about himself. There's disagreement about those prophecies, but generally it is agreed that at least he must be a born man in the line of David.