You do have the traditions of men, and a hierarchy. You most emphatically do not have the Magisterium, though.
And your possessiveness of the Bible does not address its origins. You have Bibles out there that are obviously theologically wrong. You have not addressed how you identify Biblical correctness.
The Bible is correct because God ordained that God's Church would and did accept it. There may be minor variations in different translations, but I've never come across anything earth shattering. The essence is still there in most major translations. But if you are talking about such things as the Mormon Bible, then it is wrong because God's Church did not accept it.