Final answer:
Congress exercises oversight of the executive bureaucracy through hearings, investigations, and reviewing agency actions, rather than by directly managing agencies, passing executive orders, or appointing heads of agencies.
Step-by-step explanation:
Congress is most likely to exert oversight of the executive bureaucracy through hearings, investigations, and review of agency actions. This form of oversight is significant in a democracy with a system of checks and balances. Congressional oversight is vital to scrutinize the performance and legality of the executive branch's activities. The legislature uses various mechanisms to monitor and control the extensive federal bureaucracy. Congress controls funding, approves presidential appointments, and conducts hearings that can range from standard inquiries to intense probes into agency operations. These oversight activities help maintain a balance of power, prevent corruption, and ensure government accountability.
While direct management of agencies is not typically a congressional role, passing legislation provides the legal framework for agencies to operate within. Although legislative oversight does involve legislation, it doesn't encompass issuing executive orders, which is a presidential power. Additionally, Congress does not appoint agency heads but exercises the power to confirm or reject the president's appointments, adding another layer of oversight. The review of agency actions through hearings and investigations is a direct and transparent method for Congress to hold the executive accountable, making it the most likely way that Congress exercises its oversight role.