Though many people argue that bureaucracy is influencing the branches of government, it's not an actual branch of the government. The argument about bureaucracy is supported by the unofficial "fourth branch of government," which refers to those outside the three branches who influence decisions and the people.
The press is often considered part of the fourth branch, sometimes being specifically called the fourth branch because of their public influence, according to Wikipedia. Bureaucratic influence does have a major impact on how laws are enacted or enforced, but it's not always representative of the wants of America's citizens. Bureaucracy is often blamed for slow or difficult processes within the federal government.