I’d like to respond to this question by first rewording it a bit. Rather than responding to the question, “How much of the Bible should a person know before accepting Jesus as their Savior?”, I would like to respond to the question, “How much of special revelation must a person know before accepting Jesus as their Savior?” With this, I’m simply substituting “special revelation” for “the Bible”. In defending my reason for this substitution comes my response to the question.
The primary reason I wish to substitute special revelation for the Bible is because if we limit the dialogue to the Bible, then it would be impossible for Early Church believers, including the disciples of Christ, to be saved (as the New Testament wasn’t written at that point). It was knowledge of the person and work of Jesus Christ (also defined as special revelation) that is necessary for salvation. I believe that knowledge can come through various forms of special revelation alongside of the Bible. This does not mean to infer that these forms are equal to the Scriptures, rather, that other forms of special revelation can be used as a means for communicating the critical information necessary for conversion while being subordinate to the authority of Scripture.
Another dynamic at work in answering this question is the work of the Holy Spirit in the process of salvation. Salvation is primarily the work of the Holy Spirit (some argue that it is the Holy Spirit alone). Simple exposure to the specially revealed truths of Scripture that are necessary for salvation is not sufficient. It is an exposure paired with a repentant heart, which is made possible only through the work of the Holy Spirit.
After defining the function and means of special revelation as pertains to conversion, the knowledge necessary for salvation (which could be communicated via various forms of special revelation), I believe can be limited to four points. Each point highlights a Biblically defined (especially by Romans and other Pauline Epistles) dynamics at work in a comprehensive soteriology; namely, (1) Original Sin, (2) Justification, (3) Sanctification and (4) Glorification.
Original sin – knowledge and regretful recognition of sins and the sin nature along with its effects on human life.
Justification as pertains to both (a) knowledge of the person of Jesus Christ (namely his identity being characterized by a dual human/divine nature necessary for reconciliation between man and God) and (b) knowledge of the salvific work of Jesus Christ with special attention lent to his crucifixion (substitutionary death) and resurrection (hope for new life).
Sanctification – knowledge of the role and work of the Holy Spirit in regenerating the believer through restoration the Divine image characterized by faith, love and obedience
Glorification – knowledge of the hope of the glory and life of God to be manifest in the life of the believer beginning with conversion and continuing on until eternity.
It seems that with the elimination of any of these 4 points would mean an insufficient framework for conversion. I would hope that it also seems that while the necessary points are limited to four, that we need not add another. I believe these four points present the necessary information for conversion as revealed specially by God through His written and Living Word.