[From The Catholic Answer Bible (2002). I wrote the 44 apologetics inserts, which can be purchased by themselves for $2.99.]
The Assumption can easily be reconciled with Scripture because it is not contrary to it in any way. The premise that all Christian doctrines must appear in Scripture in order to be accepted cannot itself be found anywhere in Scripture. Catholics agree that no Christian teaching can contradict anything in the Bible. The Assumption of Mary is a belief of this sort.
We believe in it as part of the received Tradition, passed down from the apostles, and because it is utterly plausible and consistent with Mary‟s role as the Theotokos (“God-bearer”) and immaculate sinless one, who was granted a singular grace from God in order to bear God Himself in her body.
If indeed she was free from sin, then it follows that she would not undergo the decay of death, which was the penalty for sin (Gen 3:16-19). But for the Fall of man, no one would have died. Mary is the exception, for very good reason, and the forerunner of the resurrection that all who are saved will experience (1 Cor 15:12-23; cf. Mt 27:52-53). Moreover, there are parallels in Holy Scripture of others going straight to heaven (bodily) without dying: Enoch (Heb 11:5; cf. Gen 5:24), Elijah (2 Ki 2:1, 11), and many during the Second Coming (1 Thes 4:15-17).
Pope Pius XII, in his Apostolic Constitution, Munificentissimus Deus, of November 1, 1950, proclaimed this dogma in the following words:
By the authority of our Lord Jesus Christ, of the blessed apostles Peter and Paul, and by our own authority, we proclaim, declare and define as a dogma revealed by God: the Immaculate Mother of God, Mary ever Virgin, when the course of her earthly life was finished, was taken up body and soul into the glory of heaven.
Lk 1:28-31 with Zeph 3:14-17
1 Cor 15:26
2 Cor 12:2-4
Rev 12:1, 5, 17
Catechism of the Catholic Church: 966, 974
Bible on Mary’s Assumption