A good discussion of the different ways in which this term is applied can be found here: http://theconversation.com/what-is-anarchism-all-about-50373.

To quote a relevant passage: "Anarchism is a process whereby authority and domination is being replaced with non-hierarchical, horizontal structures, with voluntary associations between human beings."

If bureaucratic complexity is the complexity of the structures that organize our society, its existence is entirely consistent with an anarchist society. The structures would no longer be hierarchal, but anarchism makes no claim that organization (or the complexity associated with it) shouldn't exist.

From my understanding, Anarchists look at an power structure and ask how does it legitimize it's existence. If it was put in place by the people and not some unaccountable body, then it is ok to have it, otherwise it needs to be dismantled and or replaced. (This is a very, very simplified look at a very narrow aspect of anarchism of course.)

For example a lot of decisions in Anarchist communities will be driven by arriving at consensus of all concerned by the decision, instead of a "mob rule of the majority" like in Democratic voting process.

The way you arrive at the decision is a bureaucratic process if you will, that the community has agreed upon.

That's my take on it