Where in the Bible is there mention of the idea that all Christian truth can be found in the Bible? Obviously nowhere, since that idea didn't exist until 1,500 years later. Where in the Bible is there mention of a book called "The Bible"? Maybe you should have asked "does the Bible include any references to the doctrine of Purgatory as accepted by the early Church?" Yes. It does.
First, we know that not every person dies in a state of complete spiritual purity. Yet the Bible tells us that nothing tainted can come into God's presence (Rev 21:27). Therefore one must conclude either (1) that every person who is not in a state of perfect spiritual purity at the moment of death goes directly to hell, or (2) that God provides a means of final purification for those who have not rejected Him, but who are still tainted with the effects of sin, before they come into His presence. That means is called Purgatory - a place or state of final purgation, or purification.
Luke describes Jesus's metaphorical teaching about our final judgement ...
"For while you are going with your opponent to appear before the magistrate, on your way there make an effort to settle with him, so that he may not drag you before the judge, and the judge turn you over to the officer, and the officer throw you into prison. I say to you, you will not get out of there until you have paid the very last cent." (Luke 12:58-59)
The phrase "throw you into prison" could refer to hell - except for one thing. It speaks of getting out once we have paid what is due, and no-one gets out of hell, ever. Therefore it is clear that at judgment we are declared either lost or saved, but some of those who are saved do not enter heaven immediately, but only after they have been cleansed of the spiritual baggage they have brought with them.
After his death, Christ went to a place where the saved were waiting, and told them the good news that heaven would now be opened to them. (1 Pet. 3:19). These people were not in heaven, but obviously were not in hell. Were they in Purgatory? This is not certain; but it makes clear that a temporary place where the saved await their entrance into heaven was accepted by the early Church and does not in any way conflict with the Christian teaching of heaven and hell as the only final destinations.
Christ refers to sinners who "will not be forgiven, either in this age or in the age to come" (Matt. 12:32). Obviously then forgiveness or purgation must be possible in the age to come (after death); otherwise this statement by Christ would be meaningless.
The Bible tells us that we will each be judged on the quality or completeness of our response to Christ . And what happens if a person has failed to respond fully, and has not done all Christ has called him to do? By the mercy of God he can still be saved! BUT "only as through fire" (1 Cor 3:15). Fire is repeatedly used in Scripture as a metaphor for purification, the way impurities were burned out of gold. This passage is clearly speaking of something that happens after death. Where does this "fire-like" purification take place? Not in heaven certainly, since there is no suffering there, and "fire" obviously suggests suffering. But surely not in hell, since those in hell have no hope of salvation. The only possible place this passage could refer to is what we now call "Purgatory". Paul believed in it, or he would not have written the above.
I assume you are using an incomplete Protestant Bible, but if you were using the original Bible, the complete Bible used by every Christian on earth until a few hundred years ago, you could read the following ...
"... he acted in a very excellent and noble way, inasmuch as he had the resurrection of the dead in view; for if he were not expecting the dead to rise again, it would have been useless and foolish to pray for them in death. But if he did this with a view to the splendid reward that awaits those who had gone to rest in godliness, it was a holy and pious thought. Thus he made atonement for the dead that they might be freed from this sin" (2 Macc. 12:43–45).
This text indicates that the chosen people, even before the birth of Christ, prayed for those who had died, a practice which continued in the early Christian Church. We know this from multiple Christian writings of the second century and subsequent time points. Obviously there is no need to pray for people who are in heaven; and it is pointless to pray for people in hell. Therefore the Church's practice of praying for the dead from the very beginning reveals their belief that some of the deceased were in a place other than heaven or hell. This passage also indicates that the living can help the deceased by praying on their behalf - a truth that Christ's Church still teaches today, just like every belief of the Apostles and the early Church.