Building the Next Generation of Federal Employees Act This bill expands access to federal internships, provides for an internship preference, and allows for federal agencies to reimburse student interns for expenses. Specifically, the bill requires the Office of Personnel Management (OPM) to: establish an internet platform to serve as a centralized resource for federal internship opportunities; carry out a pilot program to engage individuals from underrepresented demographics for possible participation in the civil service; establish the Pathways Program to promote federal employment to students and recent graduates by excepting program participants from competitive service requirements; and establish the Federal Fellowship and Scholarship Center within the OPM to manage all executive branch fellowships and internships. The bill also increases the number of recent college graduates that an agency head may hire through expedited hiring authority, creates a competitive hiring preference for former interns and fellows, and alllows executive agencies to reimburse student interns for transportation and subsistence expenses.