Freedom to Move Act This bill directs the Department of Transportation to award competitive five-year grants (i.e., Freedom to Move Grants) to states, local governments, transit agencies, and nonprofit organizations in both rural and urban areas to cover the lost fare revenue for fare-free public transportation and improve public transportation. Grants must be used to support (1) implementing a fare-free transit program; and (2) efforts to improve public transportation, particularly in underserved communities, such as costs associated with efforts to provide more safe, frequent, and reliable bus service, including bus stop safety and accessibility improvements, and pedestrian and bike shelters.