To add on to this, I learned earlier today that the Ethiopian Bible has 84 books, whereas the Bible we use in the West only has 66. Did they just have access to documents that the early Church did not? Or were those books excluded for a reason?
Let's head back to 325 AD, and check out the Byzantine Empire. Constantine is the emperor, the most famous of the Byzantines by a wide stretch. Some forty years prior, Diocietian divided the Roman Empire into two pieces, taking the Eastern Roman Empire (which would be the Byzantine Empire) for himself, and giving Maximian control of the West. He'd soon appoint two Caesars, to create the Tetrarchy, dividing the Empire into four core regions, with one of the two Caesars administrating a significant chunk of each of the two Empires. Constantine inherited the western Roman Empire when his father died in 306. Constantine immediately set about changing the world in ways that would echo throughout history.
He introduced a wide range of political and economic reforms, and re-unified the Roman Empire. He refounded Byzantium, which gives the Byzantine Empire its name, and moved his capital there. It would later be renamed Constantinople after him.
While all of this is going on, an offshoot of a fairly minor religion is spreading throughout the Empire. Christianity is a young faith, and is only recently beginning to be viewed as a faith all its own. It's wildly different from most religions throughout the empire, but one thing that's similar is a lack of theological conformity. This caused a significant amount of infighting, sometimes literally, and was causing unrest, as was the general persecution of the Christians.
Constantine responded in a few ways. In 312, he was, himself, baptized. In 313, he pushed for the Edict of Milan, which made Christianity a tolerated faith in the empire, and would (in theory) curb persecution. Finally, he convened the first Council of Nicaea in 325, which was a gathering of Christians from throughout the Empire dedicated to trying to codify the young faith. The most notable accomplishment of the Council for purposes of this question was the creation of a closed canon. This essentially means that it established the idea that there was a correct theology, and that this correct theology could be established, and should be vetted by central authority. The Council didn't yet establish the Pentarchy, the five Popes who would govern Christendom from a spiritual perspective, but it did begin to make feelers towards what the central authority should look like, designating the different sectors of the Empire into "metropolitans". This concept was one of the most critical goals of the Council; a lot of people were writing a lot of things about Christianity, and there were some vastly differing theological ideas being bandied about. Establishing what is, and what is not, compatible with Christianity was the key goal of this meeting, and they sought to exclude certain ideas from the canon.
So, immediately following the Council, we have the idea that there should be a Closed Canon, and we have some general authority on who establishes it; the three cities of Rome, Antioch, and Alexandria being the most influential.
However, the three different Popes of those cities didn't fully agree on what books should be included in the Canon. On top of that, the Ethiopian delegation (then known as Aksum), didn't agree with the definition of the Trinity as laid out by the Council, and didn't fully adopt the various decrees of the Ecumenical Councils. I'm not fully an expert of the historical evolution of the Coptic Church, but it would grow out of a combination of the Alexandrian See and the Ethiopian Orthodox movement. This is the bible you've heard of with 84 books, and the earliest reference I'm familiar with is the letters of Athanasius the Confessor, who was an Alexandrian Pope, in 367.
The Catholic Bible would be established by the Council of Rome in 382, and confirmed by Hippo and Carthage late that century. This was largely comprised of the Roman Pope and his bishops.
The Eastern Orthodox Bible is based on the Seventh Ecumenical Council (and the last), the Second Council of Nicaea in 787 AD. This was an Ecumenical Council, meaning it included both the Orthodox and Catholic representatives, though the Catholics voiced fairly strong opposition to some of the decrees resulting, which would contribute to the Great Schism of 1054.
So, who wrote the Bible? Various people, usually councils of religious elders designated as authoritative by the Ecumenical Conventions initiated by Constantine the Great with the goal of unifying Christianity and establishing a singular canon that would be acceptable both to the leaders of the faith and to the empire. Was anyone missing any documents? Maybe, but it’s important to remember that the goal was to take a prolific quantity of writings with a very wide range of ideas and cut it down in scope to only represent a single closed canon. Exclusion was the point.
Sources:
Canons of Council of Rome, 382 (having trouble finding a translation online on a reputable site)
Eusebius's Pamphlets, including a history of the early church prior to the Council of Nicaea and a biography of Constantine
The Age of Constantine: Change and Continuity in Administration and Economy