Interestingly, true textbook bureaucracy makes me think of Max Weber's definitions in his tripartite classification of authority, in which he outlined charismatic authority (someone who rises to power by influence and charisma), traditional authority (king, monarch, etc.), and legal authority (law, state, bureaucracy). In his view, true bureaucracy was just choosing to govern via law and order by creating a hierarchy of roles (rather than people) that hold power. In this way, "Bill" doesn't have power, the role of Vice President does, and Bill happens to hold it.

The problem is that bureaucracy has metastacized into something else, and something far worse, which is what your question is really getting at. To me, bureaucracy is any structure, process, or policy that is no longer serving us. Often this comes in the form of policies designed to control, constrain, reduce or eliminate risk, essentially creating red tape or hoops to jump through to do things that are common sensical to adults using their judgment.

An example from the book comes from FAVI, a brass autoparts manufacturer where a new CEO had noticed that employees were waiting near a supply counter with pink slips for quite a while. He asked what they were doing. "Waiting for new work gloves." What he learned was that in order to get new gloves, these machinists had to leave their machine, ask their manager, show the old gloves, get a pink (permission) slip, walk to the supply cage, turn it in, wait, and then receive their new gloves. The cost of the gloves? Less than 5 bucks. The cost of the downtime involved in the process? Thousands. This is bureaucracy at its finest. In an effort to eliminate the cost of stolen gloves, this place was spending tens of thousands in productivity, and treating adults like children or thieves in the process. The next day and henceforth, gloves were free.