Most of the women we know of specifically came from a wealthier Roman background. This isn’t really surprising considering the resources necessary for setting up a monastic community, or even for establishing oneself as a secluded ascetic. Pilgrimage to holy sites, an important facet of devotion for many Christians in this time period regardless of gender, was yet another significant drain on personal resources. It’s also worth pointing out that wealthier people were more likely to write and be written about. With the notable exception of Mary of Egypt, most of these women were quite well educated.
Similarly, few of these women took the religious path alone. Paula and her daughter Eustochium and Macrina the Younger and her mother Emmelia were two sets of mother-daughter pairs who established their homes as monasteries for women. Melania the Younger adopted the monastic life together with her husband Pinianus. They also acted as teachers and advisors for prominent male Christian writers. Not only that, but it was hardly possible for a woman to go on a long pilgrimage alone. In traveling to places like Jerusalem, they brought not only family members, but entire entourages, consisting mostly of household members who had opted for the monastic life themselves.
Life of St. Macrina - Tertullian.org
McNamara, Jo Ann. "Muffled Voices: the Lives of Consecrated Women in the Fourth Century." In Distant Echoes: Medieval Religious Women Volume I, edited by John A. Nichols and Lillian Thomas Shank, 11-29. Kalamazoo, MI: Cistercian Publications, 1984.
Simpson, Jane. "Women and Asceticism in the Fourth Century: A Question of Interpretation. In Women in Early Christianity, edited by David M. Scholer. Taylor & Francis, 1993. [Parts of this book are available on Google Books here]