How do the three branches of government control the Bureaucracies?

The Congress has the power of the purse. Its budgetary power is so influential that funding of every government bureaucratic offices would be controlled by this institution.

In the same manner, the President as he is exercising his executive power where he has the supervision and control of all executive bureaus and agencies.

More over, the Supreme Court may prevent or instruct thru its judicial decisions all bureaucratic agencies about the legality of their functions and mandate to be enforced as far as governance is concerned. By virtue of Supreme Court decisions, it will become part of the law of the land under the principle of stare decisis.