Christians accept the Bible as authoritative and true for a variety of reasons.
INDIVIDUAL, PERSONAL CONVICTION
As Jesus states, "My sheep hear My voice, and I know them, and they follow Me" (John 10:27). When God brings us to Christ, we recognize our Master's message, both spoken and written. God Himself causes this to be the case. If He has chosen you to receive His mercy, you will also recognize His message.
This is personal revelation of objective truth from the only truly objective authority, God.
According to 2 Timothy 2:16-17, "All Scripture is inspired by God and profitable for teaching, for reproof, for correction, for training in righteousness; so that the man of God may be adequate, equipped for every good work." If the Bible is true, if it is scripture inspired by God, then it will be beneficial for teaching, for reproof, for correction, and for training in righteousness. It has demonstrated itself to be exactly that for thousands of years to the church as a whole, and to every individual Christian in a personal way. If your life is devoted to Christ, you too will find the Bible to be useful.
As a promise from the only objective authority, this too is objectively true.
The Bible contains multiple eyewitness testimonies of numerous events. Facts can be confirmed through the testimony of two or three witnesses, as Christ explains, "by the mouth of two or three witnesses every fact may be confirmed" (Matthew 18:16). As one example, the death, burial, and resurrection of Jesus were witnessed by many. Matthew and John, both eyewitnesses, record their versions of these events in the books of the Bible bearing their names (Matthew 27-28; John 19-21). The Qur'an, on the other hand, written centuries after the fact in a different country, denies these events (4:157).
It is objectively true that confirmation can be provided through two or more witnesses, but the perspectives of witnesses may be somewhat subjective in many cases. In this case, since the authors were writing under the influence of the authoritatively objective Spirit of God, their witness is confirmed by His objective authority and is therefore likewise objective.
God has repeatedly demonstrated His power and authority by announcing events before they occur (Isaiah 46:9-10). The suffering and crucifixion of the specific person of Christ, for example, was described (Isaiah 53, c700BC; Zechariah 12:10, c510BC) long before Christ Himself died (c30AD), with Isaiah's prophecy apparently spoken before crucifixion as a method of execution had even been invented (c600BC). Many of the prophecies of the Bible are so stunning that skeptics have claimed they must have been written after the fact, because if they had been written before the fact, they would be undeniably miraculous. These would include Daniel's prophecies of Alexander the Great (Daniel 8:21) and Antiochus Epiphanes (8:23-25), the prophecy of the coming of Josiah (1 Kings 13:2), and the destruction of the Jewish temple in 70AD (Matthew 24:2).
God Himself, the objective authority, claims that He does this, so this too is an objective criteria.
In spite of millennia of attacks on the Christian scriptures, no argument has ever been able to stand against them. If you yourself have sincerely searched and genuinely cannot find an answer to a supposed Biblical contradiction, or an attack of some other nature on the scriptures, feel free to ask.
How can we know anything at all? Every worldview or faith has some attempt at an answer to this question, but only the Bible provides an intellectually satisfying framework for knowledge.
If there were no God, we would have no authoritative promise that anything could be trusted. At best, if atheism were true, we could only promise ourselves that the laws of logic were valid. But since we know full-well that we are not in charge of the laws of logic, our promise to ourselves is empty and groundless... no more than wishful thinking. Were atheism true, then even if it were possible for us to believe something, but we would have no justification for that belief -- we would have no real reason for believing it. Without a singular sovereign God, there is no one who can truly guarantee anything. If polytheism were true, then yet again, no one could authoritatively promise us that the laws of logic are valid. We would have no grounds for believing that they are, and thus we would have no ground or justification for any belief at all. Under a monotheistic God who does not make promises about His own consistency or character, again we would have no authoritative promise that the laws of logic are valid, and all humanity's beliefs would be completely unjustified.
The Bible, on the other hand, presents a God who, when He declared His own chosen name to Moses, described Himself with a permanent guarantee that His own identity correlates exactly to His own identity, "I am who I am" (Exodus 3:14). The Law of Identity, the most basic law of thought, is practically God's proper name! He further has informed humanity that He is incapable of denying Himself (2 Timothy 2:13; cf 1 John 1:5), so if He creates something He cannot also not-create it at the same time and in the same way, guaranteeing that what is created, is created -- if it is, it is. What He causes, He causes; what He plans, He plans; what He promises, He promises. The Bible further guarantees that He will always be this way (Malachi 3:6; Psalm 55:19; Hebrews 1:12, 13:8). He is completely sovereign over all things (Deuteronomy 4:35, 4:39; Psalm 119:90-91; Ecclesiastes 11:5; Isaiah 45:5-6, 45:21-22, 46:9; Mark 12:29; John 1:3; Acts 4:12; 1 Corinthians 8:6; Ephesians 4:4-6; Colossians 1:16-17, 2:10; Hebrews 3:4, 6:13), so His promises are authoritative, and it is utterly impossible for Him to lie (Titus 1:2; Hebrews 6:18; John 14:6; Numbers 23:19; Proverbs 8:8-9; 1 Samuel 15:29), so His promises can always be trusted. Further, God has informed humans of these very promises from the moment of our creation, such that all people have an innate knowledge of them (Romans 1:20), which explains why even those who have never read the Bible, including atheists, know and completely trust these promises inscribed on their consciousness by their authoritative Creator.
If the Bible is true, it is possible to actually know something -- to have a justified, true belief. Under other worldviews, knowledge itself is not possible, because no belief has any more justification than any other belief. Objectivity itself can only be known if the God of the Bible is genuine.
The Bible offers the only possible source of knowledge. It has withstood every attempt to demolish it. It was written by eyewitnesses, contains fulfilled prophecy, and offers practical wisdom and guidance for every-day living.
What's more, God has provided in the Bible a clear message about you. You are a sinner -- you have done things that you should not have done (Romans 3:23). Because of this, you don't deserve the life you live (Romans 6:23). But you can be forgiven if you trust in the person of Jesus (Romans 10:9-10).
Naturalism does not accept the authority of any text as sacred. All knowledge claims are fallible and correctable. They have to be testable and verified by many people, and the more this is the case for any given claim, the more we trust it; whereas the less this is the case, the less we trust it.
Our criteria are as objective as we can confirm any criteria to be: evidence observable, directly or indirectly, actually or in principle, by everyone, and conclusions drawn from that evidence that obey all the requirements of valid logic (and thus do not succumb to any known fallacies or errors of reasoning).
For more on this see Part II ("How We Know") of Sense and Goodness without God (pp. 21-62).