Transportation Security Screening Modernization Act This bill directs the Transportation Security Administration (TSA) to streamline the process for individuals applying for or renewing enrollment in multiple security threat assessment (STA) programs, in particular the Transportation Worker Identification Credential (TWIC) and the Hazardous Materials Endorsement (HME) programs. Among other things, the TSA must permit an individual to enroll at a TSA-authorized enrollment center once and use the application, as well as information generated by TSA’s vetting, to enroll in any other programs; permit an individual to enroll in more than one STA program at the same time for a single fee that is less than the combined fee for applying to the same programs separately; provide for a streamlined and expeditious renewal process; and provide states the expiration dates for each individual’s STA to ensure commercial driver's licenses include an individual's current HME status. Additionally, the TSA must publish on its website information relating to the streamlining of the enrollment system. If the TSA determines it is necessary to implement these changes through rulemaking, the bill provides for an expedited rulemaking process.