Every worldview, when reduced to its most basic fundamentals, requires self-attestation, or, in other words, a "circular argument".
Such arguments are necessary for every worldview. For example, a rationalist (someone who accepts reason as the supreme authority) can only attempt to justify his reliance on reason by... using reason.
Christianity, likewise, has a supreme authority, and that authority is God. He has given us His Word and told us to use it as our basis for understanding.
The Bible claims to be "inspired by God and profitable for teaching, for reproof, for correction and for training in righteousness" (2 Timothy 3:16). It repeatedly claims to state verbatim the Word of God (Exodus 4:22, 5:1, 7:17; Joshua 7:13, 24:2; Judges 6:8; 1 Samuel 2:27, 10:18; Acts 21:11; etc).
Thus, for Christians, the only way to "prove the Bible" is by... using the Bible.
The Christian faith states that the Bible is self-attesting. So, as the rationalist puts his faith in reason because he believes reason tells him to, we put our faith in the God of the Bible because the God of the Bible tells us to. There simply is no higher authority to which we can appeal.
(If this sounds silly, I would challenge you to analyze your own beliefs, find your own most basic fundamentals, and see if you can find something more authoritative than them by which to derive their authority. Of course, if you could find anything more authoritative than your basic fundamentals, your basic fundamentals would NOT BE your basic fundamentals.)
The Bible claims that the God who speaks through it cannot lie (Hebrews 6:18) and that He is never wrong (1 John 3:20; Job 37:16).
The Bible also claims that it is "living and active and sharper than any two-edged sword, and piercing as far as the division of soul and spirit, of both joints and marrow, and able to judge the thoughts and intentions of the heart" (Hebrews 4:12).
The Bible's God declares "My word... will not return to Me empty, Without accomplishing what I desire, And without succeeding in the matter for which I sent it" (Isaiah 55:11).
Thus, since the Bible claims to be God's Word and His Truth, then when it claims to pierce your soul and spirit, to judge your thoughts and intentions, and to accomplish its purpose, it will in fact pierce your soul and spirit, judge your thoughts and intentions, and accomplish its purpose. This will demonstrate its self-attestation.
However, not everyone chooses to accept the authority of the message of scripture, in spite of its impact on their life. As Jesus put it in John 10, "But you do not believe because you are not of My sheep. My sheep hear My voice, and I know them, and they follow Me".
The Apostle Paul agrees in 1 Corinthians 1:18, "For the word of the cross is foolishness to those who are perishing, but to us who are being saved it is the power of God".
For some, the message will be a cornerstone to support your life. For others, it will be a rock of stumbling (Isaiah 8:14).
Beyond the personal impact that scripture will have on your life, recognize that without the truth of scripture to lean on, human experience becomes unintelligible. Without the Creator God, there can be no creation. Without His eternal, timeless and unchanging character, there can be no possibility of knowledge. Without His moral code and perfect justice, there can be no such thing as absolute morality. Without His own perfect sacrifice in Christ, love loses all definition.
The authority of the scriptures can be determined from the fact that without them, there would ultimately be no authority at all. Or, to put it another way, the scriptures are self-attesting in that they must be true because of the impossibility of the contrary.