She attended Dayton Academy and graduated from high school in Atlanta. She attended the Pratt Institute"s School of Information and Library Science in New York and graduated in 1904.
A prominent librarian during the first half of the 20th century, she worked for (and eventually led) the New Jersey Public Library Commission for 37 years. The New Jersey Public Library Commission hired Askew on January 1, 1905, assigning her to travel among the state"s libraries to introduce them to modern library practice and to set up a summer training program for New Jersey librarians. She was to be their "organizer and missionary" to "get libraries going," as there were only 66 libraries in the state at that time.
With the exception of her time as a reference librarian at the New Jersey State Library in Trenton from 1909-1915, Askew worked for the New Jersey Public Library Commission for the entirety of her career.
There, she established a county library program, created as a regional approach to serve towns that could not support local libraries on their own. She eventually oversaw the establishment of 12 county libraries herself.
Askew worked to increase the effectiveness of public libraries. In 1906, she founded a summer school for the staff of small libraries to share knowledge and skills.
Concerned with providing books to rural areas still without a local or county library, Askew began sending "traveling libraries" - shipments of around 300 books - to community buildings throughout the state.
She began shipping specific collections to libraries in New York and Connecticut by 1913, an early example of interlibrary loan. In 1920, Askew designed one of the earliest bookmobiles in the United States.A., driving her Ford Model T to carry materials to people who did not have access to a library. During World War I, Askew organized a program to send books overseas to military camps and hospitals.
During World World War II, she helped to organize a Victory Book Campaign.
She wrote frequently and published scholarly articles and books, including The Place, the Manitoba and the Book (1916). Throughout her career, she was supported in her cause by the State Teachers" Association, the Federation of Women"s Clubs, state and local grange groups, and others
The campus library at William Paterson University was named in her honor for some time. Askew worked for the commission until her death in 1942 and resided in Trenton, New Jersey.
By 1942, there were 316 local libraries in the state of New Jersey.
Askew served as president of the New Jersey Library Association (1913-1914 and 1939-1940), vice-president of the American Library Association (1938-1939), chairwoman of children"s reading for the National Congress of Parents and Teachers (1924-1929), and was a member of the Trenton Board of Education (1923-1933).