Access, Success, and Persistence in Reshaping Education Act of 2017 or the ASPIRE Act This bill amends the Higher Education Act of 1965 by requiring the Department of Education (ED) to rank institutions of higher education (IHEs) based on the percentage of first-time, full-time students who receive Pell Grants and are enrolled at the IHEs. The IHEs in the bottom 5% must improve the enrollment of those students by specific deadlines or pay a fee-per-student penalty. Additionally, ED must rank IHEs based on the percentage of first-time, full-time students who enroll at the school and graduate within 6 years. The bill gives IHEs in the bottom 5% the option of receiving funding to improve student graduation rates. Those IHEs must improve those rates by specific deadlines or pay a penalty. The bill establishes consumer warning requirements for IHEs with low enrollment or graduation rates. ED must establish: (1) grant programs for improving graduation rates, and (2) a bonus program for providing nonfinancial rewards to IHEs that make college more affordable and increase college access and success for low-income or working class students and moderate-income students. ED must collect the penalty fees and use them to fund the grant and award program.