Promoting Robust Opportunities for Minority Institutions and Strengthening Entrepreneurship Act or the PROMISE Act This bill requires the Small Business Administration (SBA) to report on various aspects of its relationship with historically black colleges and universities (HBCUs), including the number of small business development centers located at HBCUs, the number of women's business centers and Veteran Business Outreach Centers that have partnerships with HBCUs, and the number of hours of training and education provided by a program overseen by the Office of Entrepreneurial Development of the SBA to students and graduates of HBCUs. In addition, the SBA is directed to promote entrepreneurship and small business opportunities at HBCUs by conducting outreach and providing access to programs, resources, and opportunities offered by the SBA.