In July, 1907, Burwell was appointed to a "human computer" position at Mount Wilson Observatory. In 1910, she attended the fourth conference of the International Union for Cooperation in Solar Research, when it was held at Mount Wilson.
Burwell specialized in stellar spectroscopy. She was solo author on some scientific publications, and co-authored several others (some of which she was lead author), with notable collaborators including Dorrit Hoffleit, Henrietta Swope, Walter S. Adams, and Paul W. Merrill.  With Merrill she compiled several catalogs of Be stars, in 1933, 1943, 1949, and 1950. She also helped to tend the Mount Wilson Observatory Library. She retired from the observatory in 1949, but continued speaking about astronomy to community groups. She also published a book of poetry, Neatly Packed.