Barry was the second child born to Jeremiah and Mary-Ann Bulkley, and was given the name Margaret Anne. Mary-Ann Bulkley was the sister of James Barry, a celebrated Irish artist and professor of painting at London's Royal Academy. Jeremiah Bulkley ran the weigh house in Merchant's Quay, Cork. However, anti-Catholic sentiment led to his dismissal from this post. This and subsequent financial mismanagement left Mary-Ann and Barry without the support of either Jeremiah Bulkley (whose debts led to him spending time in the Marshalsea debtors' prison in Dublin) or later the Bulkleys' married son John. A third child appeared in the Bulkley family and was named Juliana. Although presented as being Barry's sister, it is likely that she was Barry's daughter as a result of childhood sexual assault, as the charwoman who discovered Barry's sex when laying out the body stated that pregnancy stretch marks were present.