The scripture you quoted later in your post was deemed "God's word" by people just like these bishops. My question, which nobody has been able to answer, is this: how do we know that those who canonized the Bible didn't "have absolutely no way of knowing" as you put it?
Actually, Protestants have the harder time making their case, because as one convert to Catholicism points out, nowhere in Scripture is it written, "Sola scriptura." Also, as John Donne remarks in one of his sermons, the first Christians had to ask the Jews, "Which books were the scriptures?"
Catholics believe that God guides His Church to the Truth, and therefore when the Church decided that certain books were canonical and which were not (effectively decided at least as early as St. Jerome but not formally confirmed until the Council of Trent), they had divine guidance. Similarly the writers of the various biblical books were divinely guided.
There is, of course, no way to prove this unless you have faith, something Protestants and Catholics agree on. But I would find it hard to study history and not conclude that God intervened in history, first to the Jews and then to Christians. Both the Jewish and Christian stories are firmly anchored in history, although it's possible to be a skeptic and disbelieve it.
G-d dictated the Torah to Moses letter for letter, and Moses wrote it down.
The Prophets were written under the influence of Prophetic visions, which is a lower form of revelation than the Torah.
The Ketuvim were written under Ruach HaQodesh, which is lower still.
Then chr*stianity came along and mucked everything up, which causes people like you to be smart-asses.
The authentic Bible was canonized by the Men of the Great Assembly ('Anshei-HaKenesset HaGedolah) and not by any bishops of any church. Everything else is an imposition.