It is certainly wonderful to see you undertake this to better understand the Catholic virewpoint.  I will do my best to give the
Scriopture references that would indicate a state of final purification, or sanctification, prior to our entrance into the Kings

    As you noted, you will not find the word "purgatory" in 'any' Bible, but you can find the truth of purgatory there.

    Let us start with a few Biblical truths.  The first of which is Revelation 21:27 "nothing unclean can enter (heaven.)"  By this we understand for us to see God "face to face", we must "be perfect as your Heavenly Father is perfect."  But how, you may ask, can this happen to we sinful human beings?     We believe this because God does not merely impute Christ's righteousness to us, but actually infuses His life into our soul
making us 'pleasing' to God.  1 Peter tells us we become "partakers of the divine nature", yes Christ comes and dwells within us, perfecting us in this life, thus preparing us for the next life.  Yet, we fail in many aspects of our walk with the Lord, and these failures (refusal of the grace God has given us) puts up barriors, or roadblocks on our way to perfection.  These failures come because we love ourselves more than we love God.  Our goal as Christians is to die totally detached from creatures and this world, thus totally in love with God.  Unfortunately, when most of us die, we will still have this inordinate attachment to
creatures, and not the Creator.  But by the grace and power of the cross, God has provided what Catholics call purgatory as a place where the  love of God will burn away all those affections for creatures, so we can come to see the beatific vision, that is
God, face to face!  Were it not for this cleansing, most of us would not be able to 'handle' the grandeur and majesty of the

    Now, let's look at the texts Catholics use most often to explain Purgatory.

    For no other foundation can any one lay than that which is laid, which is Jesus Christ. Now if any one builds on the foundation with gold, silver, precious stones, wood, hay, straw -- each man's work will become manifest; for the Day will disclose it, because it will be revealed with fire, and the fire will test what sort of work each one has done. If the work which any man has built on the foundation survives, he will receive a reward. If any man's work is burned up, he will suffer loss, though he himself will be saved, but only as through fire.  1 Cor 3:11-15 (RSV)

    Here is a passage where Paul speaks of the "day" a reference to our judgement after this life. He says if your works aren't of a certain quality, they will be burned up.  Now note what he says next, the person "will suffer loss, though he himself will be saved, but only as through fire."  So, not only will the works be burned up, but this person will SUFFER LOSS.  Now, no one suffers in heaven, and those who suffer in hell cannot be saved, so that leaves this 'other' place, or 'state', as the Church defines it, which we call Purgatory.

    The next text to look at is Matt 5:23ff: " So if you are offering your gift at the altar, and there remember that your brother has something against you, leave your gift there before the altar and go; first be reconciled to your brother, and then come and offer your gift.
 Make friends quickly with your accuser, while you are going with him to court, lest your accuser hand you over to the judge, and the judge to the guard, and you be put in prison;
26 truly, I say to you, you will never get out till you have paid the last penny.   Matt 5:23-26 (RSV)
    This is another allusion to our judgement before God, represented as the judge here.  The passage says to settle while ON YOUR WAY to court with him.  Thus, the next verses assume you didn't settle with him in this life, analogously.  You are then handed over to the guard to be put in prison.  The prison must be hell, then, right?   Wrong, for the passage continues on saying "you will never get out till you have paid the last penny" thus assuming that when you HAVE paid that last penny, you will be released.  No one gets released from hell, and heaven is definitely not a prison, so again, you have this third place we call Purgatory.

        There are other passages that give this same teaching.  Luke 12:42-48 speaks of the master giving one servant a severe beating, and the other a lesser beating.  Luke 12:56-59 reiterate what Matt 5:23ff taught.  Matt 18:21-25 speaks of the same
type of punishment.  Hebrews 12:23 speaks of the "spirits of just men made perfect" and we would emphasize the "made perfect" part of that verse.   Note, they were already just, but needed to be made perfect.  Matt 12:32 speaks of the sin against the Holy Spirit which will not be forgiven in "this age or in the age to come."  There seems to an assumption made by Jesus that there are sins that CAN be forgiven in the age to come, but the sin against the Holy Spirit is not one of them.

    Purgatory, when properly understood, in no way detracts from the finished work of Christ.  if you think about it, if Christ's work was truly 'finished' in the protestant understanding, then we wouldn't need to do anything!  Not even accept Him as Lord
and Saviour!  Yet, we all know that is a prerequisite for entering heaven.  In a similar way, as I explained above, Purgatory shows forth the power of once for all sacrifice at Calvary, as it says that mercy continues even beyond the grave, so that those of us who haven't been made  "perfect as your Heavenly Father is perfect" on earth can become one of the "just men made perfect" through the fire of God's love in Purgatory!