Burns was the fourth of eight children. Fortunate to have a father who believed in educating children of both sexes, Burns in 1902 graduated from Vassar College in Poughkeepsie, New York. Over the next seven years, she did graduate work in linguistics, first at Yale University in New Haven, Connecticut, and then—after a hiatus during which she taught English at Erasmus Hall, a public high school in Brooklyn—at the Universities of Berlin, Bonn, and Oxford. In England, having become interested in the struggle to secure the vote for women, she soon left school to work full-time for her chosen cause. As a close colleague of suffragist leaders Emmeline (Pankhurst, Emmeline) and Christabel Pankhurst (Pankhurst, Dame Christabel Harriette), Burns earned a special medal from the Pankhursts' Women's Social and Political Union for the bravery she exhibited in the course of several arrests and prison hunger strikes.

Burns returned to the United States in 1912. There, together with Alice Paul (Paul, Alice), she began a fight for a constitutional amendment to guarantee women's right to vote. In 1913 they formed the Congressional Union for Woman Suffrage, which was succeeded three years later by the National Woman's Party. Burns helped organize political campaigns, edited The Suffragist, and spent time in jail for infractions ranging from covering Washington, D.C., sidewalks with chalked suffragist messages to organizing a demonstration against President Woodrow Wilson during World War I.

Although Burns's fiery oratory gave the impression of indefatigability, the struggle exhausted her. After the ratification of the Nineteenth Amendment on August 26, 1920, Burns retreated from political activism. Returning to Brooklyn to live with two unmarried sisters, she went on to rear a newborn niece left motherless in 1923 by the death of Burns's youngest sister in childbirth. Burns never returned to the fray. Taking solace in her commitment to Roman Catholicism, she died in 1966 after a long decline.