She was born Annie Willis Dallas in Nashville, Tennessee, in 1876 to a distinguished upper-class family. Her father, Trevanion B. Dallas, had moved to Nashville in 1869 and established himself as an entrepreneur in the textile industry. Her grandfather, Alexander J. Dallas, had been a commodore in the U.S. Navy, while his brother, George M. Dallas, served as Vice President of the United States under James K. Polk. Annie Dallas was educated at Ward's Seminary and Price's College for Young Ladies, both in Nashville. In 1902, in a quiet ceremony at Christ Church Cathedral, she married Guilford Dudley, a banker and insurance broker. Together they had three children, Ida Dallas Dudley, who died in infancy, Trevania Dallas Dudley, and Guilford Dudley, Jr..
A few years after being married, Anne Dallas Dudley became involved in the temperance movement as a supporter of alcohol prohibition. Through her work in the temperance movement and her association with friends such as Maria Daviess and Ida Clyde Clark, Dudley became convinced that women's place in society could only be improved if women were allowed to vote. At the time, however, a majority of men and women opposed the idea of women participating in the political process. In September 1911, Dudley, Daviess, Clark, and several other women met in the back parlor of the Tulane Hotel and founded the Nashville Equal Suffrage League, an organization dedicated to building local support for women's suffrage while "quietly and earnestly avoiding militant methods". Dudley was selected as the organization's first president. During her presidency, the league organized giant May Day suffrage parades, usually led by Dudley and her children. Dudley also helped bring the National Suffrage Convention to Nashville in 1914. At the time, it was one of the largest conventions ever held in the city. After serving as president of the local league for four years, Dudley was elected to head the Tennessee Equal Suffrage Association in 1915. During this time she helped to introduce and lobby for a suffrage amendment to the state constitution. Although the amendment was defeated, a later measure to give women the right to vote in presidential and municipal elections was eventually passed by the state legislature in 1919. In 1917, Dudley became the Third Vice President of the National American Woman Suffrage Association, where she contributed significantly to advancing legislation on the issue of women's suffrage. In 1920, Dudley, along with Catherine Talty Kenny and Abby Crawford Milton, led the campaign in Tennessee to approve ratification of the Nineteenth Amendment to the US Constitution. On August 18, Tennessee became the 36th and deciding state to ratify the amendment, thereby giving women the right to vote throughout the country.
Later life
Following the success of the suffrage campaign, Dudley became the first woman associate chairman of the Tennessee Democratic Committee. She was also selected as the first female delegate-at-large to the Democratic National Convention in 1920. Dudley's involvement in politics declined significantly in subsequent years, with her efforts being focused on civic and charitable causes during the remainder of her life. She was an active worker for the American Red Cross during World War II and later served as board chairman of the Association for the Preservation of Tennessee Antiquities. Dudley died unexpectedly on September 13, 1955, of a coronary occlusion at her home in Belle Meade, Tennessee. She was 78 years old. She is buried with her family at Mount Olivet Cemetery in Nashville.