Hapgood was born in Boston, the descendant of a long-established New England family. She studied Germanic and Slavic languages, specializing in Orthodox liturgical texts. She was one of the major figures in the dialogue between Western Christianity and Orthodoxy. She traveled through Russia between 1887 and 1889. While there, she spent several weeks with the famous Russian novelist Leo Tolstoy on his country estate. She wrote a lengthy article detailing her visit and observations of the man trying to live his ideal life for The Atlantic magazine, it was published in 1891.
In 1893 she reviewed a book by Kate Marsden which described her journey across Russia to find a cure for leprosy. Marsden was lauded by the Royal Geographical Society, but Hapgood joined a campaign to belittle her efforts. Later speculation suggests that Hapgood may have been driven by the notion that Marsden was writing about her country or because of the rumours about Marsden which may have initiated homophobic motives in Hapgood.
She was in Moscow when the revolution broke out in 1917, but was able to escape and returned to the United States.
Despite Count Tolstoy's admonition that she should marry, Ms. Hapgood never married and had no children. She died in New York.