Catholics believe that at the end of her life, Mary was taken, body and soul, into heaven by the power of her Son. This doctrine is called the Assumption of Mary. It is NOT called the Ascension of Mary, because that would mean she went by her own power, which is not the case.
The Bible does not explicitly mention this event. However, it does say that both Enoch and Elijah were assumed into heaven (Heb. 11:5, 2 Kgs. 2:11) and that the bodies of saints left their tombs after the Resurrection (Matthew 27:52-53). So it would not be unheard of if the body of Jesus' sinless mother was not also saved from corruption in the grave. History also suggests an assumption, because nobody can point to a place where her body is buried.
- Immaculate Conception and Assumption - Nihil Obstat and Imprimatur (catholic.com)
- Understanding the Assumption and Queenship of Mary - Starts at the very beginning - trusting the Church, and continues on to the Assumption. Download as a pdf; by Steve Ray (catholic-convert.com)
- Assumptions About Mary - A convert from Evangelicalism/Fundamentalism examines the Assumption - very thorough; by T.L. Frazier (catholic.com)
- How to Argue for Mary's Assumption - Answers to common questions; by Jason Evert (catholic.com)
- Her Assumption Befits the Mother of God - By Valentine Long (catholicculture.org)
- Assumption of Mary - From the Catholic Encyclopedia (newadvent.org)
- Mary's Death and Bodily Assumption - By Lawrence P. Everett (catholicculture.org)
- The Assumption of the Blessed Virgin Mary - From Juniper Carol's Mariology (bringyou.to)
- The Assumption/"Queen of Heaven" [10 min] - Covers the basics; by OneTrueChurch
- Mary's Assumption Into Heaven - Quotes by early Church Fathers - see Part IV (scripturecatholic.com)
- Mother of Christ, Mother of the Church - From the Catechism, see #966 (vatican.va)
- The Woman of Revelation 12 - Is this Mary? By Jimmy Akin (catholic.com)