Why isn't the word 'Trinity' in the Bible?

That's true—the word never appears in Scripture. But plenty of important theological words work this way: "Bible" itself isn't in the Bible, and neither is "monotheism" or "incarnation." These are summary terms later writers coined to describe a pattern of teaching found throughout the text, not phrases the text needed to use itself.

The word "Trinity" comes from the Latin trinitas, which the early theologian Tertullian used around the year 213. An earlier Greek term, trias, appears even sooner, used by Theophilus of Antioch around 180. Both were coining vocabulary to summarize something Christians already found throughout Scripture: one God, described in passages that also speak of Father, Son, and Holy Spirit each as fully God.

So the term is a later label for an earlier pattern, not a later invention with no biblical basis—those are two different claims, and only the first one is actually true.