Interesting question.
It seems that a major part of the 'bible' was already in existence - what we now call the Old Testement.
And what's now in the New was FOUGHT over (by Catholics) as to which writings would be included or tossed.
To say that ONLY the Roman church would have collected and assembled the NT is, by definition, boastful and arrogant.
Much like the whine of the OT prophet who was convinced that ONLY he was left to carry on GOD's work.
He soon found out; from GOD; that there were a VAST number (7,000 I think) of His followers around that Jezebel was NOT trying to kill!
The Bible, or what most Christians of any denomination consider Scripture, consists of both the Old and New Testaments. Without an organization with sufficient authority to rule on the canon of the NT, we would have only the OT now.
Only the Catholic Church existed at the time, and just as the Apostles went through a process of discernment of issues, which some might call FIGHTing, so was there discussion about which books should be included in the NT. The Apostles, and by definition their spiritual descendants, were given the authority by Christ to bind and loose to make decisions such as this.