Buses United for Safety, Regulatory Reform, and Enhanced Growth for the 21st Century Act or the BUSREGS21 Act This bill addresses provisions related to passenger motor carriers, including school buses. Among other matters, the bill prescribes requirements for, and limitations on, the use of Department of Transportation (DOT) motor coach carrier safety fitness determinations; exempts commercial motor coach drivers, motor coach carriers, and private school bus carriers from certain proposed regulations and requirements, including requirements related to obstructive sleep apnea, and the installation of speed limiting devices; requires DOT to establish a committee to modernize Federal Motor Carrier Safety Administration (FMCSA) regulations applicable to the operations of passenger motor carriers; requires the Government Accountability Office to conduct a study assessing the effects of FMCSA and National Highway Traffic Safety Administration regulations affecting certain small fleet motor carriers that were finalized in the preceding ten years; directs DOT to carry out a pilot program to compare the effectiveness of prescheduled inspections with random destination inspections on passenger motor carriers; prohibits DOT from promulgating any new regulatory mandates for motor coaches or school buses that are not based solely on sound data and science that will directly reduce crashes; and creates an incentive program for public transit agencies that contract with the private sector for fixed route bus transportation services.