According to the Bible, Mary is not explicitly mentioned after Acts. There is no record of her death or non-death. Further, since she was very young when she gave birth, it is conceivable that she would have outlived many of the original authors. Either way, any information about Mary after about 40 AD cannot rest on Biblical justification.
And I think that an important point to emphasize: There is no outright biblical justification that Mary did *anything* after Acts. Anyone who claims otherwise is presenting not scripture, but an interpretation of scripture.*
Strictly speaking the Church's teaching is ambiguous as to whether Mary was assumed into heaven in the manner of Elijah, or if her body was taken to heaven afterwards (as was the case with Moses). Neither opinion is excluded specifically, but the general thought in the West was that Mary was assumed just before she would have died normally.
This thought is based on several facts. One is the authority of the Church — while this is not something that was held to be official dogma until relatively recently, the consistent and near unanimous opinion of the church Fathers was that Mary's body is currently in heaven. This is no doubt supported by the fact that there is no tomb and no shrine which claims to hold the bone of Mary (this is conspicuous because all of the Apostles had such sepulchers). Further, it was promulgated as doctrine by the Pope resting on Papal authority. In addition, there is an ancient document which actually relates the death of Mary and the assumption of her body.
So you have several sources who agree:
- Ancient legends
- Theological consensus
- No physical tomb
- Papal authority
Now, while it is possible to disagree with one or more of these, it is beyond the scope of this question to address such issues.
* While it may be reasonable to believe that Mary breathed, ate, drank, and eventually died, there is no commentary on these in the Bible. If we exclude all evidences outside of the Bible, there is no way to say that she did not join the Judaizers or that she performed miracles as great as the signs in the Gospels.