What are the existing checks on the exercise of bureaucratic power?

The main checks on the bureaucracy come from the elected
parts of government.  Specifically, both the Congress and the president have ways to
check the exercise of bureaucratic power.

The president can
check the bureaucracies by appointing high level bureaucrats.  These appointees are
supposed to control the bureaucrats below them and keep them from exercising too much
power.  At the same time, the president makes the departments' budget requests.  The
president can stop requesting money for agencies and programs he does not like.  This
prospect keeps bureaucrats from just doing whatever they
want.

The Congress has the power of oversight over
bureaucracies and, most importantly, the power of the purse.  If the Congress does not
like what an agency is doing, it can call bureaucrats before hearings and scold them. 
The bureaucrats need to pay attention to what Congress says because Congress is the body
that determines how much money each agency actually gets.  Congress can also change the
laws under which the agencies work.  This is another check on the bureaucracy because
Congress can make new laws affecting agencies that act in ways Congress does not
like.

In these ways, the elected parts of government have a
lot of control over the bureaucracies.  When bureaucrats exercise "too much" power it is
because the elected bodies allow them to do so.