Reduce Bureaucracy Act This bill prohibits certain political appointees from serving in career positions in federal agencies. Specifically, the bill prohibits current and former presidential appointees, cabinet officials, and other senior officials from serving in career-appointment (i.e., permanent) positions in executive agencies without the approval of the Office of Personnel Management (OPM). Agencies must certify that the appointment is necessary in order for the agency to meet its mission and the OPM must determine that the appointment process was fair, open, and free from political influence in order to approve a request. OPM must also transmit approved requests to specified congressional committees before issuing final approval to agencies. The bill also prohibits political appointees from serving in career positions for two years after their departure, and directs the OPM and the Office of Management and Budget to take any actions necessary so as to limit the number of political appointees to 2,000.