Your claim is that the Bible teaches that God is three distinct personalities, i.e. the Father, the Son and the Holy Spirit.

In the Old Testament, God's name is mentioned often. It is YHWH. This has been translated as LORD in most English Bibles. However, it is not a title, it is a name...

Exodus 3:15:
God also said to Moses, "Say this to the people of Israel, `The YHWH, the God of your fathers, the God of Abraham, the God of Isaac, and the God of Jacob, has sent me to you': this is my name for ever, and thus I am to be remembered throughout all generations.

Exodus 15:1-3
"I will sing to the YHWH, for he has triumphed gloriously; the horse and his rider he has thrown into the sea. The YHWH is my strength and my song, and he has become my salvation; this is my God, and I will praise him, my father's God, and I will exalt him. The YHWH is a man of war; the YHWH is his name.

Exodus 33:19-20 And he said, "I will make all my goodness pass before you, and will proclaim before you my name `The YHWH'; and I will be gracious to whom I will be gracious, and will show mercy on whom I will show mercy. But," he said, "you cannot see my face; for man shall not see me and live."

Deuteronomy 4:12-19 Then the YHWH spoke to you out of the midst of the fire; you heard the sound of words, but saw no form; there was only a voice. And he declared to you his covenant, which he commanded you to perform, that is, the ten commandments; and he wrote them upon two tables of stone. And the YHWH commanded me at that time to teach you statutes and ordinances, that you might do them in the land which you are going over to possess.
"Therefore take good heed to yourselves. Since you saw no form on the day that the YHWH spoke to you at Horeb out of the midst of the fire, beware lest you act corruptly by making a graven image for yourselves, in the form of any figure, the likeness of male or female, the likeness of any beast that is on the earth, the likeness of any winged bird that flies in the air, the likeness of anything that creeps on the ground, the likeness of any fish that is in the water under the earth. And beware lest you lift up your eyes to heaven, and when you see the sun and the moon and the stars, all the host of heaven, you be drawn away and worship them and serve them, things which the YHWH your God has allotted to all the peoples under the whole heaven.

Zechariah 14:9
The YHWH will be king over the whole earth. On that day there will be one YHWH, and his name the only name.

But certainly the Bible also teaches that Jesus (a man) was God, right?

Job 25:2-6 "Dominion and fear are with God; he makes peace in his high heaven. Is there any number to his armies? Upon whom does his light not arise? How then can man be righteous before God? How can he who is born of woman be clean? Behold, even the moon is not bright and the stars are not clean in his sight; how much less man, who is a maggot, and the son of man, who is a worm!"

Numbers 23:19 God is not man, that he should lie, or a son of man, that he should repent. Has he said, and will he not do it? Or has he spoken, and will he not fulfil it?

Was Jesus really claiming to be the same being as this YHWH?

John 8:28-30 So Jesus said, "When you have lifted up the Son of man, then you will know that I am he, and that I do nothing on my own authority but speak thus as the Father taught me. And he who sent me is with me; he has not left me alone, for I always do what is pleasing to him." As he spoke thus, many believed in him.

John 8:42-43 Jesus said to them, "If God were your Father, you would love me, for I proceeded and came forth from God; I came not of my own accord, but he sent me. Why do you not understand what I say?

Yes, you can assume that Jesus' was hinting, and making suggestions that he was God. However, it's obvious to see that he was denying such an idea. The fact is that some of these verses have to be interpreted figuratively, in order to understand them.

Either the YHWH of the Old Testament was speaking figuratively, or Jesus was speaking figuratively. Without the understanding that parts of the Bible are meant to be figurative, it will not make sense at all.

Who do you suppose was speaking figuratively, YHWH or Jesus?

John 16:25
These things have I spoken unto you in proverbs (figuratively): but the time cometh, when I shall no more speak unto you in proverbs (figuratively), but I shall shew you plainly of the Father.

The time will come when Jesus will speak plainly about WHO? About the Father. About God, about YHWH.

About the plural 'We' used in the Old Testament is a well known issue to anyone who understands the Semetic languages. There is a plural of number, and there is a plural of respect. Even old English uses this, like when the Queen says "We are not amused!"

Using this to prove multiple gods, or multiple persons within God, is not clear enough to overcome the much more exact numerical description of God given in the Bible.

Mark 12:29-30 Jesus answered, "The first is, `Hear, O Israel: The Lord our God, the Lord is one; and you shall love the Lord your God with all your heart, and with all your soul, and with all your mind, and with all your strength.'