From Blood and Milk:

Bureaucracy, is the core of an organization. It’s what keeps an organization functioning when its staff changes. Without the forms and the regulations, you don’t have an organization. You have a cult. The structures are what makes it about more than just whoever works there at the moment. Bureaucracy puts the “organize” into organization.

That does not mean, however that bureaucracy should rule your work. It’s supposed to help the work get done. The work does not come second. And everyone accepts that.

Her distinction between bureaucracy and process seems one of goals. If I'm reading this correctly, the author is saying that process is for the sake of a structure beyond the immediate implementation, bureaucracy is metascaffolding (including process) set up for the sake of implementation success, and therein lies the difference.

It's unfortunate both words are sufficiently loaded in my mind that I'm unable to think as clearly as I'd like about this. Will keep a lookout for ways to fix that.