Advancing Inclusion and Representation in the Workforce of Aviation and Transportation Systems Act or the AIRWAYS Act This bill directs the Department of Transportation (DOT) to establish a program to provide grants to support the education and recruitment of an aviation workforce (i.e., aircraft pilots, aviation maintenance technical workers, and aviation manufacturing technical workers). Eligible applicants include certain educational institutions (e.g., an institution of higher education, a postsecondary vocational institution, and a local educational agency), state or local governments, and nonprofit organizations. In addition, air carriers in a partnership with certain educational institutions are eligible for aircraft pilot workforce grants. Among other things, DOT must give priority to applicants that assure that grant funds will be used to encourage the participation of populations that are underrepresented in the aviation industry, including women, minorities, and individuals in economically disadvantaged geographic areas and rural communities.