Bran is what is left when a grain is stripped back, and for a very long time removing it was the whole point of milling. White flour was more expensive, kept better and signalled a household that could afford it, and the bran went to animals.
The reversal, in which the discarded fraction became the interesting one, happened over roughly a century and involved millers, doctors, food reformers and eventually breakfast manufacturers, mostly arguing past one another.
Milling technology set the terms
Roller milling made very white flour cheap and consistent for the first time. A product that had been a luxury became the default, and the distinction between fine and coarse flour stopped being a matter of money.
It is hard to overstate how much of the subsequent argument was really about that machine. Once separation was easy and total, the question of whether it ought to be done at all could finally be asked.
The reformers and their vocabulary
Nineteenth-century food reformers made whole grain a moral cause, and their language is closer to preaching than to description. They wrote about purity, simplicity and plainness, and their objection to white bread was as much about refinement in the social sense as in the milling sense.
That vocabulary stuck. A great deal of later writing about coarse and fine grains reuses the reformers' framing without noticing where it came from, which is why the subject still carries an odd note of virtue.
Bulk as a description
The older technical term was bulk, and it described a physical property: material that passes through largely unaltered and adds volume. It is a plain, mechanical description, and it is the part of the story that has held up best.
The commercial history and the descriptive history are worth keeping apart. One is about what a mill does to a grain; the other is about what people have wanted that to mean.