Where in the Bible does it tell us that the Bible is the only or ultimate source of authority? I cannot find it anywhere! II Timothy 3:16 is the closest, but it does not say only! Where in history, the Bible, or the writings of the early Church was this concept ever taught? Since the church did not have a complete Bible until hundreds of years after Christ ascended to heaven, how did the early church teach and spread Christianity?
Because a particular idea is not expressed in the Bible in precisely the wording desired, it does not mean the concept does not exist.
The source of authority is God, the Father. He then gave His authority to the Son. "And Jesus came and spoke to them, saying, 'All authority has been given to Me in heaven and on earth'" (Matthew 28:18). (See also I Corinthians 11:3; 15:23-28.) The true question, then, is "Through what means has Christ chosen to make his will known to mankind?"
Jesus told his disciples that they would not be left on their own. "However, when He, the Spirit of truth, has come, He will guide you into all truth; for He will not speak on His own authority, but whatever He hears He will speak; and He will tell you things to come. He will glorify Me, for He will take of what is Mine and declare it to you. All things that the Father has are Mine. Therefore I said that He will take of Mine and declare it to you" (John 16:13-15). By the command of Christ, these things were then to be taught to the nations. "Go therefore and make disciples of all the nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all things that I have commanded you; and lo, I am with you always, even to the end of the age" (Matthew 28:19-20). The apostles accomplished this duty, "Now we have received, not the spirit of the world, but the Spirit who is from God, that we might know the things that have been freely given to us by God. These things we also speak, not in words which man's wisdom teaches but which the Holy Spirit teaches, comparing spiritual things with spiritual" (I Corinthians 2:12-13). Paul told the Ephesian elders, "I have not shunned to declare to you the whole counsel of God" (Acts 20:27).
Notice that this directly contradicts the questioner's assertion that church did not have the complete council of God until hundreds of years after Christ assended. Instead, Peter claims "Grace and peace be multiplied to you in the knowledge of God and of Jesus our Lord, as His divine power has given to us all things that pertain to life and godliness, through the knowledge of Him who called us by glory and virtue, by which have been given to us exceedingly great and precious promises, that through these you may be partakers of the divine nature, having escaped the corruption that is in the world through lust" (II Peter 1:2-4). Since all things pertaining to life and godliness has come through the knowledge of God, this does not leave anything left to be said. Paul makes much the same point. "All Scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness, that the man of God may be complete, thoroughly equipped for every good work" (II Timothy 3:16-17). "Scripture" is the written words of God. Since the Scripture equips a man for every good work, what good work is absent from the Scriptures? The answer must be "none!"
The apostles knew that they would not always be present. They knew that God's teachings needed to be recorded as a constant reminder to those who followed. "Therefore, brethren, be even more diligent to make your call and election sure, for if you do these things you will never stumble; for so an entrance will be supplied to you abundantly into the everlasting kingdom of our Lord and Savior Jesus Christ. For this reason I will not be negligent to remind you always of these things, though you know and are established in the present truth. Yes, I think it is right, as long as I am in this tent, to stir you up by reminding you, knowing that shortly I must put off my tent, just as our Lord Jesus Christ showed me. Moreover I will be careful to ensure that you always have a reminder of these things after my decease" (II Peter 1:10-15). The apostle John said much the same, "That which we have seen and heard we declare to you, that you also may have fellowship with us; and truly our fellowship is with the Father and with His Son Jesus Christ. And these things we write to you that your joy may be full" (I John 1:3-4).
Since the apostles have a complete account of all that Jesus taught them via the aid of the Holy Spirit, it becomes important that no one alter this message to mankind. Peter warned, "For we did not follow cunningly devised fables when we made known to you the power and coming of our Lord Jesus Christ, but were eyewitnesses of His majesty ... And so we have the prophetic word confirmed, which you do well to heed as a light that shines in a dark place, until the day dawns and the morning star rises in your hearts; knowing this first, that no prophecy of Scripture is of any private interpretation, for prophecy never came by the will of man, but holy men of God spoke as they were moved by the Holy Spirit" (II Peter 1:16, 19-21). The words delivered by the apostles were not their own opinions by the words of God. As Paul told the Galatians, "But I make known to you, brethren, that the gospel which was preached by me is not according to man. For I neither received it from man, nor was I taught it, but it came through the revelation of Jesus Christ" (Galatians 1:11-12). And once delivered, they were not to be altered. "I marvel that you are turning away so soon from Him who called you in the grace of Christ, to a different gospel, which is not another; but there are some who trouble you and want to pervert the gospel of Christ. But even if we, or an angel from heaven, preach any other gospel to you than what we have preached to you, let him be accursed. As we have said before, so now I say again, if anyone preaches any other gospel to you than what you have received, let him be accursed" (Galatians 1:6-9).
This does not leave any leeway. The Bible is a set standard which cannot be altered or contradicted. Hence, it is the standard by which we will be judged. Jesus stated, "the word that I have spoken will judge him in the last day" (John 12:48). These are the words which the apostles accurately and completely recorded for us. "In the day when God will judge the secrets of men by Jesus Christ, according to my gospel" (Romans 2:16).
Could there be any continuing revelation from God? It seems that such would not be possible. What is later revealed can only emphasize what the apostles taught since alterations have been ruled out by God. Nothing new can be revealed without contradicting the apostles' claim that their message was complete. But most telling is Jude's assertion. "Beloved, while I was very diligent to write to you concerning our common salvation, I found it necessary to write to you exhorting you to contend earnestly for the faith which was once for all delivered to the saints" (Jude 3). The faith, God's Holy Word, was delivered once. There would not be multiple deliveries. It was delivered for all -- for all times and for all people. There isn't one message for one nation and something else for another nation. The message doesn't change over time. What people needed to know in the first century remains the same for us in the twenty-first century.
The Bible contains all that we need to know concerning life, godliness, and salvation. Being complete and unalterable, it then is our only source for establishing what God has authorized. Those who claim the right to modify its teachings have taken on its curse (Galatians 1:8-9).