Where is the Trinity in the Bible?

The Trinity is woven right through the Bible - though not the word "Trinity," which was coined later to name a pattern already there in the text. The absence of the label is not the absence of the thing. Words like monotheism, omnipotence, and even Bible aren't in Scripture either; summary terms exist to gather up what a whole body of texts teaches.

So look at the data the word gathers. First, the New Testament is fiercely monotheistic: there is one God, full stop. Second, that one God is spoken of as Father, as Son, and as Holy Spirit, and each is treated as fully God, the Word was God in John 1, the Spirit called Lord and giver of life. Third, the three are genuinely distinct: the Son prays to the Father in Gethsemane, is sent by the Father, and promises to send another Advocate, the Spirit. One who prays to another, is sent by another, and sends another is not a single person wearing three masks. And texts like the baptism of Jesus and the closing command of Matthew 28 to baptize in the one name of Father, Son, and Holy Spirit hold all three together.

The doctrine is simply the attempt to say all of that at once without dropping any of it: one God, eternally existing as three coequal, coeternal, genuinely distinct persons. Not three gods, which would be tritheism, and not one person in three costumes, which would be modalism. Deny the word if you like; every one of the biblical givens it names remains on the page.