What is the biblical basis for the Immaculate Conception?
It is the same reason that Pope Pius IX put forth in the Apostolic Constitution Ineffabilis Deus (Latin for "Ineffable God") that defined the dogma of the Immaculate Conception of the Blessed Virgin Mary. The decree was promulgated on December 8, 1854, the date of the annual Feast of the Immaculate Conception.
Supreme Reason for the Privilege: The Divine Maternity
And indeed it was wholly fitting that so wonderful a mother should be ever resplendent with the glory of most sublime holiness and so completely free from all taint of original sin that she would triumph utterly over the ancient serpent. To her did the Father will to give his only-begotten Son -- the Son whom, equal to the Father and begotten by him, the Father loves from his heart -- and to give this Son in such a way that he would be the one and the same common Son of God the Father and of the Blessed Virgin Mary. It was she whom the Son himself chose to make his Mother and it was from her that the Holy Spirit willed and brought it about that he should be conceived and born from whom he himself proceeds.
Might we find this Supreme Reason the Divine Maternity in Sacred Scripture?
Yes from the Angel's words:
In Lk 1:32 (RSVCE)
32 He will be great, and will be called the Son of the Most High; and the Lord God will give to him the throne of his father David,
And
In Lk 1:35 (RSVCE) 35 And the angel said to her, “The Holy Spirit will come upon you, and the power of the Most High will overshadow you; therefore the child to be born will be called holy, the Son of God.
And Elizabeth filled with the Holy Spirit exclaims with a loud cry, '[a]nd why is this granted me, that the mother of my Lord should come to me?'
Thus the Supreme Reason, the Divine Maternity, is in the Bible.
And if this is true, did Mary not need to be saved from her sin?
The Catechism of the Catholic Church answers
CCC, 492 The "splendor of an entirely unique holiness" by which Mary is "enriched from the first instant of her conception" comes wholly from Christ: she is "redeemed, in a more exalted fashion, by reason of the merits of her Son".[LG 53, 56.]] The Father blessed Mary more than any other created person "in Christ with every spiritual blessing in the heavenly places" and chose her "in Christ before the foundation of the world, to be holy and blameless before him in love".[cf. Eph 1:3-4.]
Please see also CCC, 508.
If she were sinless, then why would she have suffered the consequences of sin--that of death?
This question has no scriptural grounding. Two men born with original sin have not yet died and are no longer in the world, Enoch and Elijah, and Christ the sinless one died.
The reason Mary died is linked to that of her Son.
Closing
What biblical indications are there that Mary was conceived without sin?
God through Angel Gabriel greets Mary, "Hail, full of grace1". St. John the Baptist is born sinless but is sanctified after his conception. Therefore we can deduce that Mary was always full of grace from the very first moment of her existence.
1. Grace being a supernatural gift of God, freely bestowed upon us for our sanctification and salvation, Mary is therefore fully sanctified and fully saved.
What is now revealed in the New was hinted at in the Old:
Song of Solomon 4:7 (RSVCE)
7 You are all fair, my love; there is no flaw in you.
Please see also Ineffabilis Deus | Apostolic Constitution issued by Pope Pius IX on December 8, 1854 starting from Interpreters of the Sacred Scripture. - The entire Apostolic Constitution is very fruitful reading.