Ashe joined the University of Minnesota Medical School in 1992 as an assistant professor of neurology. She has also worked with the Minneapolis Veterans Affairs Health Care System. She was the founding director of the N. Bud Grossman Center for Memory Research and Care.  As of 2022, she has received over $28million in grants from the U.S. National Institutes of Health.
The Minneapolis Star Tribune described Ashe as a "distinguished professor considered by many to be on the short list for a Nobel Prize for her work".