The word "Trinity" is not in the Bible. However, the theological concept of the Godhead is found in the Bible.
There is unity in the Godhead both in creation and human salvation. It’s in the Bible, Hebrews 1:1-3, NKJV. "God, who at various times and in various ways spoke in time past to the fathers by the prophets, has in these last days spoken to us by His Son, whom He has appointed heir of all things, through whom also He made the worlds; who being the brightness of His glory and the express image of His person, and upholding all things by the word of His power.”
The Spirit of God is also involved in this world’s creation. It’s in the Bible, Genesis 1:1-2, NKJV. "In the beginning God created the heavens and the earth. The earth was without form, and void; and darkness was on the face of the deep. And the Spirit of God was hovering over the face of the waters."
In creation God refers to Himself in the plural. It’s in the Bible, Genesis 1:26, NKJV. "Then God said, "Let Us make man in Our image, according to Our likeness.”
God the Father is involved in both creation and salvation through Jesus Christ. It’s in the Bible, Colossians 1:13-17, NKJV. "He has delivered us from the power of darkness and conveyed us into the kingdom of the Son of His love, in whom we have redemption through His blood, the forgiveness of sins. He is the image of the invisible God, the firstborn over all creation. For by Him all things were created that are in heaven and that are on earth, visible and invisible, whether thrones or dominions or principalities or powers. All things were created through Him and for Him. And He is before all things, and in Him all things consist.”
It was God the Father Who provided us salvation through His Son. It’s in the Bible, John 3:16, NKJV. "For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish but have everlasting life.”
The Holy Spirit was also involved in Jesus Christ coming to this earth. It's in the Bible, Luke 1:35, NKJV. "And the angel answered and said to her, 'The Holy Spirit will come upon you, and the power of the Highest will overshadow you; therefore, also, that Holy One who is to be born will be called the Son of God.'"
Jesus spoke of the unity between Him and the Father. It's in the Bible, John 16:26-2, NKJV. "In that day you will ask in My name, and I do not say to you that I shall pray the Father for you; for the Father Himself loves you, because you have loved Me, and have believed that I came forth from God.
It's in the Bible, John 14:8-10, NKJV. "Philip said to Him, 'Lord, show us the Father, and it is sufficient for us.' Jesus said to him, 'Have I been with you so long, and yet you have not known Me, Philip? He who has seen Me has seen the Father; so how can you say, 'Show us the Father'? Do you not believe that I am in the Father, and the Father in Me? The words that I speak to you I do not speak on My own authority; but the Father who dwells in Me does the works.'”
Both the Father and the Holy Spirit are in union with Jesus Christ in salvation for humanity. It’s in the Bible, John 14:13-17, NKJV. "And whatever you ask in My name, that I will do, that the Father may be glorified in the Son. If you ask anything in My name, I will do it. "If you love Me, keep My commandments. And I will pray the Father, and He will give you another Helper, that He may abide with you forever — the Spirit of truth, whom the world cannot receive, because it neither sees Him nor knows Him; but you know Him, for He dwells with you and will be in you.”
It's in the Bible, John 14:26, NKJV. "But the Helper, the Holy Spirit, whom the Father will send in My name, He will teach you all things, and bring to your remembrance all things that I said to you.”
It's in the Bible, John 16:7-11, NKJV. "Nevertheless I tell you the truth. It is to your advantage that I go away; for if I do not go away, the Helper will not come to you; but if I depart, I will send Him to you. And when He has come, He will convict the world of sin, and of righteousness, and of judgment: of sin, because they do not believe in Me; of righteousness, because I go to My Father and you see Me no more; of judgment, because the ruler of this world is judged.”
Our bodies are the temple of the Holy Spirit as part of our salvation. It’s in the Bible, 1 Corinthians 6:19-20, NKJV. "Or do you not know that your body is the temple of the Holy Spirit who is in you, whom you have from God, and you are not your own? For you were bought at a price; therefore glorify God in your body and in your spirit, which are God's.”
Look how closely we are being built into a union with Jesus Christ and the Holy Spirit. It’s in the Bible, 1 Peter 2:4-11, NKJV. "Coming to Him as to a living stone, rejected indeed by men, but chosen by God and precious, you also, as living stones, are being built up a spiritual house, a holy priesthood, to offer up spiritual sacrifices acceptable to God through Jesus Christ. Therefore it is also contained in the Scripture, "Behold, I lay in Zion a chief cornerstone, elect, precious, and he who believes on Him will by no means be put to shame." Therefore, to you who believe, He is precious; but to those who are disobedient, "The stone which the builders rejected has become the chief cornerstone," and "A stone of stumbling and a rock of offense." They stumble, being disobedient to the word, to which they also were appointed. But you are a chosen generation, a royal priesthood, a holy nation, His own special people, that you may proclaim the praises of Him who called you out of darkness into His marvelous light; who once were not a people but are now the people of God, who had not obtained mercy but now have obtained mercy.”
Jesus Christ’s last commission to His church includes all three members of the Godhead. It’s in the Bible, Matthew 28:18-20, NKJV. "And Jesus came and spoke to them, saying, "All authority has been given to Me in heaven and on earth. Go therefore and make disciples of all the nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all things that I have commanded you; and lo, I am with you always, even to the end of the age." Amen.”
The culmination of salvation is found in the unity of God’s people with Jesus the Christ just as He is in union with the Father. It was for this that Jesus prayed. It’s in the Bible, John 17:20-23, NKJV. "I do not pray for these alone, but also for those who will believe in Me through their word; that they all may be one, as You, Father, are in Me, and I in You; that they also may be one in Us, that the world may believe that You sent Me. And the glory which You gave Me I have given them, that they may be one just as We are one: I in them, and You in Me; that they may be made perfect in one, and that the world may know that You have sent Me, and have loved them as You have loved Me.”
The Godhead has worked together in our creation and salvation and will closely united with humanity through all eternity. It's in the Bible, John 14:1-3, NKJV. "Let not your heart be troubled; you believe in God, believe also in Me. In My Father's house are many mansions; if it were not so, I would have told you. I go to prepare a place for you. And if I go and prepare a place for you, I will come again and receive you to Myself; that where I am, there you may be also.”