I don't really think Orwell is making fun of bureaucracy very much in this book. The only place I can really think of where he does this is when he talks about the reports and figures that are cranked out to show that the farm is doing well. For example, we see this happen at the beginning of Chapter 8.
However, I think this is making fun of the way that governments use statistics to try to bend the truth. This is not so much an indictment of bureaucracy as it is a criticism of governments that do not tell the truth.
I suppose you can also look at the part where the animals are organizing all kinds of committees like the one promoting clean tails for cows. But that's making fun of communist efforts to improve everything through self-help more than making fun of bureaucracy.