That was certainly true but just because a local bishop deemed something "inspired" didn't make the writing inspired. It was the Church that sorted out what was inspired from what wasn't. That's all they did.
That's all they did, HD, the "Church" was where the bishop was. This is still true today. The final authority in the Church is a bishop. You are thinking of an "organization" called the Church. That is a communion of bishops who share the same faith.
This organization developed into archbishoprics as a matter of administrative workload and eventually the historical churches became patriarchates based on apostolic honor and imperial dignity of the city in which the church was located.
It was very much a bishop, usually someone who was taught by one of the apostles still alive who collected the books (scrolls) and those were the scrolls that were read. If they were read in a church, they were considered "scriptural" by that particular bishop and in that particular church.
Don't forget that until the second century there were only bishops and deacons; priests, who are really bishops assistants, or deputies if you will, have no power of their own but only through a bishop. And the priests (ierei) appear in the second century as the church began to expand.
To this day in Orthodox churches, the priest can serve liturgy only on a specially signed cloth which is issued as an authorization for the priest to do this in his name. A priest by himself has no authority, so whatever is done in a church is done by permission of the bishop, and in strict obedience to the bishop who is seen as executing the office of the Apostle he succeeded.
So, when you look at the process of canonization of the bible you find how different churches used and read different scrolls. The oldest complete bible (C. Sinaiticus) dating to mid 4th century contains two non-canonical books.
the "Church" (a communion of bishops in this case) agreed eventually on what books are "scripture" and which are not. It took them 300 plus years to do that. And even then it wasn't fully agreed upon.