What is the major power congress has over the bureaucracy?

The "power of the purse" ---congress can withhold funds from any sector of the bureaucracy which is why the agencies try so hard to influence Congress.

In fact, Congress has the power to abolish government agencies and department and eliminate jobs filled by bureaucrats.

( They don't because government workers are also voters and campaigners and there as now so many of them that they can swing elections. Congressmen want to keep their jobs as much as the bureaucrats want to keep theirs. )