Hi Jeff, while I can accept the idea that many might be in heaven who did not encounter the Bible, or even know about Jesus, I still can't agree with your Title. I do agree with your sub-title because salvation truly derives from relationship.
The point is about relationship. Unless you know someone, you don't and can't have a relationship with them. The Bible is God's Word to humanity and it's the ONLY reliable source for understanding God and learning what He requires of us. Salvation rises from love, seeing God's love, then responding with love to Him. Without the Bible one is navigating the ocean without a map or compass, while riding in a boat that's full of leaks.
You mention many other sources for what amounts to common religious thought, but many, perhaps most of those sources are severely compromised with corrupted notions that do not coincide with the words of God. Many religious sources deny God's power, and fail to point the reader to Jesus as the only hope for salvation. Worse yet, most of those sources teach a form of idolatry -- that you can earn your way to heaven by being "good."
Romans 10:12-17
12 For there is no difference between the Jew and the Greek: for the same Lord over all is rich unto all that call upon him.
13 For whosoever shall call upon the name of the Lord shall be saved.
14 How then shall they call on him in whom they have not believed? and how shall they believe in him of whom they have not heard? and how shall they hear without a preacher?
15 And how shall they preach, except they be sent? as it is written, How beautiful are the feet of them that preach the gospel of peace, and bring glad tidings of good things!
16 But they have not all obeyed the gospel. For Esaias saith, Lord, who hath believed our report?
17 So then faith cometh by hearing, and hearing by the word of God.
If a person in today's world relies upon those other sources alone, they are in effect, following people (instead of God) who may or may not actually know God or have a relationship with Him. That will result in thousands who did what you've suggested, but in the judgment, will be told, "I know you not."
Acts 17:11
11 These were more noble than those in Thessalonica, in that they received the word with all readiness of mind, and searched the scriptures daily, whether those things were so.
1 Peter 1:3-10
3 Blessed be the God and Father of our Lord Jesus Christ, which according to his abundant mercy hath begotten us again unto a lively hope by the resurrection of Jesus Christ from the dead,
4 To an inheritance incorruptible, and undefiled, and that fadeth not away, reserved in heaven for you,
5 Who are kept by the power of God through faith unto salvation ready to be revealed in the last time.
6 Wherein ye greatly rejoice, though now for a season, if need be, ye are in heaviness through manifold temptations:
7 That the trial of your faith, being much more precious than of gold that perisheth, though it be tried with fire, might be found unto praise and honour and glory at the appearing of Jesus Christ:
8 Whom having not seen, ye love; in whom, though now ye see him not, yet believing, ye rejoice with joy unspeakable and full of glory:
9 Receiving the end of your faith, even the salvation of your souls.
10 Of which salvation the prophets have enquired and searched diligently, who prophesied of the grace that should come unto you:
Those words from the Bible have life, the words and ideas from other books, other people, lack this direct connection with God's life and inspiration. We, if we are Christian, NEED God's word direct to our hearts.
Our only safe course, the only safe course to recommend to others, is that the Bible must be their only source of belief and knowledge of God. Even then we MUST ask God to guide our study, or Satan is only too willing to disrupt our understanding so that we end up following a lie, or becoming overcome with discouragement. Satan quoted the scriptures in the attempt to cause Jesus to sin. Jesus knew the scriptures, and didn't get tricked into sin.
The Bible has numerous examples of people who followed wrong advice because they misunderstood words from God. The first example is of Eve! Adam knew better so made a wrong choice, going against his conscience and deliberately against God's word by accepting the fruit from his wife.
The Bible is a "Must Read" source for any who aspire to following Christ. It's not optional in the least. The only exception I can accept is for one who is born in a place where the Bible does not exist, and yet they respond to the promptings of the Holy Spirit and end up having that relationship with God that saves. In our world, we can't get there without the Bible.