Here is the short answer – it is not in the Bible
The Assumption of the Blessed Virgin Mary was declared in 1950 by an infallible (protected from error) statement of Pope Pius XII 71 years ago.
What is papal infallibility? It is the teaching, particularly laid down at the First Vatican council 150 years ago, that Pope’s have the ability to declare something infallibly (protected from error)
So where is the Pope’s ability to teach infallibly in the Bible – Here is the short answer – it is not in the Bible
A papal teaching, even if it is declared without infallibility invoked (As all but the Assumption of the Blessed Virgin Mary have been) still require submission of intellect and will, as Pope John Paul 2 made clear when he had inserted into Canon Law “While the assent of faith is not required, a religious submission of intellect and will is to be given to any doctrine which the Pope declares upon a matter of faith and morals”
Where is that in Scripture, submission of intellect and will – again I can save you time, it isn’t
The only rebuttal to non-Catholics with questions is to point out that the Assumption isn’t in the Bible, Papal infallibility isn’t in the Bible, nor is the teaching on submission of intellect and will, even though they have all been held almost from the very moment Jesus left earth. The writings of the earliest saints in the generation following the apostles are talking about the Assumption of the Blessed Virgin Mary into Heaven, body and soul, the writings speak about papal infallibility, submission of intellect and will to the pope, and a thousand other things that are not in the Bible
The real question for those who ask where something Catholic is in the Bible is to point out that for the first 350 years or so there was no Bible, and those people, a lot of them mentioned in our Eucharistic prayer, linus, Cletus Clement Sixtus Cornelius Agatha Lucy Anastasia Lawrence Cosmas and Damian and thousands more Saints from the early Church, most of whom were martyred, they all figured it out. How? With the help of capital T tradition. As Paul tells the Corinthians “I received from the Lord what I also handed on to you.” That means oral tradition is a real thing, particularly necessary in the Early Church when there was no Bible
So you can rest assured that the Blessed Mother was definitely assumed, Body and soul into Heaven and is at the right hand of her Son Jesus, and 1,000 other things the Catholic Church teaches to be true, even though none of them are in the Bible.