I'm aware of the Vestal Virgins as a female-only, chaste religious organization that predates Christianity - but I'm a little weak on the details of how nuns themselves arose. Was it inspired by the Vestals, or just a female counterpart to the monastic movement, or what?
Nuns arose out of general monasticism. Chaste life and virginity were a late development to Christianity, Saint Paul in his epistles. Throughout history, and leading up to Saint Macrina, is actually one of the great founders of Monasticism and both male and female monastics in the East follow her rule.
Monasticism exploded in early Christianity, sometimes, especially in the Celtic Church monasteries were of mixed gender. With either an Abbess or Abbot over both genders, communities were also closely tied to them. Saint Benedict was one of the earliest western fathers of the church to develop a rule of life that men and women would follow.
However, you can also look at the freedom that Christianity offered women of all classes, both rich and poor women chose a life of monasticism because of the freedom it offered. Women were able to live independently as hermits, or within the community of a monastery.
Many Christians fled to the desert, it is claimed by some that the desert Mothers outnumbered the Fathers by double the amount (according to Mary Earle). However the vast majority of these womens were much better at hiding themselves and living away from people and received less pilgrims than the fathers did.
Female monastics flourished in large part because they wanted to avoid marriage and the "martyrdom" of being a monastic would save them from that. Source. It was also a flight from the world.
It's also important to remember that the Christians really wanted nothing to do with anything relating to paganism. SO it was a counterpart to male monastics, because in Christianity men and women were seen as equal. Monasticism is also an alternative to marriage, and since all Christians are encouraged to be chaste, there would have to be a way for both sexes to be able to live such lives.
Mary, the Mother of God, was an inspiration for such monastics, since she lived life as a virgin, (before her betrothal to Joseph, she lived in the temple, much like the Prophetess Anna). Men and women wanted to live life in imitation of her. She is the patron of all men and women who live in monasteries. I'll continue to look for more resources for you.