The French "bureaucratie" was coined in the 18th century by French economist Jean Claude Marie Vincent de Gournay, from French "bureau" (office/desk) + Greek "-kratia" (power of), as a criticism of how government over-regulation can stunt commerce.

It came into English in the early 19th century, carrying a similarly negative connotation. The connotations have shifted back and forth somewhat since then.

Still, it seems that it's never been primarily used to talk about private offices in English or French; the primary use has always referred to governments.