How can I be sure the Bible hasn’t been changed? Isn’t it just a translation of a translation of a translation, and so on?

Actually, modern translations are made from ancient copies. For example, the original Greek gospel of John was probably written at the end of the first century. Handwritten copies have survived from the second century onwards. English Bibles today use these ancient copies as a starting place. So, while it’s true that your Bible is a translation, it is not true that it’s a translation of a translation. Scholars work from the oldest manuscripts available, and in the original languages.