FYI the trinity doctrine is not specifically a biblical doctrine. It is more or less a doctrine that evolved as Christians pondered the nature of God. Early on, the new church had the idea that Jesus was more then just a man. In fact, if you recall, the Apostle Tomas called him “My Lord and my God”, or more correctly translated, “The Lord of me and the God of me”. So at the very least, one Apostle thought he was God. And when he said that, Jesus did not correct him. A very powerful scriptural witness I would say. And please don’t fall for the BS JW excuse that Tomas was just shocked and excited that he said “Oh My God!” like the expression that is commonly used today. (I used this BS explanation in field service once, and I new I was full of it even back then). Also consider that during the first century, when Tomas said this, saying such a thing as a Jew would have been considered blasphemes to say the least if it were not true.
Writings by early church Elders, some of them hand picked direct disciples taught by the Apostles, equate Jesus with God Almighty in no uncertain terms.
Again, a powerful witness.
Gradually the Holy Spirit also comes into play as indicated by these writings. So yes it would be correct to say there is no specific doctrine of the trinity in the Bible, but it is also true that all the elements of the trinity are there (Father Son Holy Spirit etc.).
And yes reading the Bible alone, as the Watchtower society correctly pointed out, would lead one to form conclusions that are part of what we call mainstream Christianity, including the idea of the trinity or at the very least that Christ was much more then just an angel as the Watchtower society presents him. On the other hand, no person ever adopts the beliefs of the Watchtower Society by reading the Bible alone, never. I hope this info helps.
Freeman