How much of Roman Catholicism is based on the Bible?

You got it backwards. The Bible is based on Catholicism. The Catholic Church compiled the Bible from its own writings, for its own use. Obviously the Church did not include in its own book anything that would conflict with its own teachings, all of which it had already been teaching for over 300 years before the Bible was compiled. Therefore everything in the Bible is in complete agreement with the teachings of the Catholic Church.