Etymonline has this to say on quarters:
"military dwelling place," 1590s, from quarter (n.) in sense of "portion of a town." The military sense is in quartermaster (mid-15c.) and might be behind the phrase give (no) quarter (1610s), on the notion of "to provide a prisoner with shelter." The verb quarter "to put up soldiers" is recorded from 1590s.
Quartermaster appears to be from something unrelated to fourths:
mid-15c., from Fr. quartier-maître or Du. kwartier-meester; originally a ship’s officer whose duties included stowing of the hold; later (c.1600) an officer in charge of quarters and rations for troops.
Although I am weak at French, it appears that quartier means area or district. Note that the dates for quartermaster are before quarter: mid-15c versus 1590s. This implies that quartermaster transferred first and then people began using quarter due to the use of quartermaster.
Transferring the meaning of quarters into a non-military dwelling place seems reasonable and, therefore, the short answer to your question is that quarters appears to have come from France by way of quartermaster.
Edit: My hunch on why quarter came from quartermaster (as opposed to Etymonline just telling us it did) is the inclusion of master in the term led people to assume that they were masters of something; it was logical to call that something a quarter. The idea of quartering up soldiers would mean to provide for them; this would be the quartermaster's responsibility. Lodging was most likely included in that and the perception of "master of lodging" makes sense.
"Women of cover" did not take. If "bush" and "bushism" are excluded from the internet search, results don't even amount to a hundred. Also, it appears to me that the prospects of it taking in the future are slim to none.
Women of cover, it seems, is a euphemism for widely used women who cover (+ their hair / head / themselves / etc.) fashioned after the widely accepted one, people of color, which in turn used to be a euphemism for "colored people." So, if people of color successfully entered the vernacular, why doesn't women of cover as well? Here's my take on it.
First, there's the fact that it looks like and smells like a euphemism, an expression used in place of one that may be found offensive or unpleasant. Euphemisms are created out of social need. That women of cover didn't take, evinces the lack of such need in the case of women who cover. (And I think we can all be glad for that.)
Secondly, even if there had been the need for such a euphemism, the syntagmatic strength of this particular one, women of cover, is so low that it could never really have harbored the expectations of succeeding. A glance at the American corpus helps to understand the underlying logic of the construction [noun denoting a person or persons] + of + [[+intensifier] noun]. For example,
"people of" is followed the most by these nouns (geographical terms excluded):
faith, god, goodwill, means, interest, wealth, conscience, integrity, power
"man of":
action, letters, god, peace, integrity, steel, science, law, principle, sorrows, faith, honor, mystery, color, courage, means, vision, europe, genius, parts, wealth, character, culture, conviction, contradictions, power, words, business, ideas, war, taste, conscience, substance, learning, reason, compassion, honesty, numbers, sense, importance, iron, knowledge, leisure
"man of many":
parts, words, hats, moods, interests, gifts, faces, contradictions, skills, voices, passions, worlds, ways, turns, turnings, trades, tensions, secrets, pitches, permutations, particulars, moves, masks, instruments, identities, guises, colors, channels, enthusiasms, dimensions, contrasts
All those nouns have something in common. They all speak either of personality traits (of merit or of demerit) or personal achievement, or of something less individual but positive (e.g. means). Also, in all of these cases, the preposition of can be replaced with have/has, has been to, has seen and such. Of cover, simply, doesn't fit the formula. That's why it sounds artificial. On the other hand, color does fit, because aside from being a physical property, it happens to have an ulterior, positive metaphorical reading (as opposed to pale blandness or black wickedness). On that note, cover too has a metaphorical reading: that of subordinance or even cowardice ("taking cover"). Another point: whenever someone speaks of values, they are referring to a value system, which means that they are familiar with that value system. That, in turn, connotes not only their knowledge of that system, but also their partaking in it. By saying that someone is of action sends a hidden message that the speaker himself values action, and by extension, might personally be or intends to be of action. Even if that happens to be obviously untrue, the message has been sent. By saying something negative about someone, the speaker avows he personally is not like that. Of cover fails miserably in this avenue as well.
These are only a few reasons why it didn't take, and why it's unlikely to. I'm sure more can be surmised.
Edit: It looks like this phrase is more than just neutrally scarce. Some actually have a problem with it:
... we would do well to heed W. J. T. Mitchell’s warning of the fallibility of pictures. Perhaps an appropriate question to ask would be, What kind of [visual] objects does the new empire produce, depend on, and desire? Given the West’s historical obsession with gender issues in Middle Eastern societies, it is no surprise that Iraqi women and their “image” have taken center stage in contemporary rhetorical battles. Seen by all as signifiers of cultural progress, Muslim women and their changing roles are often challenged and contested by their countries of origin and the West alike. They are “women of cover.” The manner in which they appear and dress in public is seen by the West as problematic and a sure sign of oppression. Their representation in Western media has been conditioned from the beginning by preconceived political ideologies and is disputed and resented by the women themselves.
Muslim Women in War and Crisis: Representation and Reality, ed. Faegheh Shirazi, ch. VIII, "Images and status. Visualizing Iraqi Women", Nada Shabout, p. 149. Unversity of Texas Press, Austin, 2010
Best Answer
The Ugly American
My sense of this is of a pejorative nature and it predates the book and the congressional record entry of 1960. But I do not purport that this answers your question.
Wikipedia relates badly behaving American travelers to Twain and D. O. Stewart. ugly American - pejorative
This ngram shows even earlier use of ugly American. I reviewed the summary of each from 1800 to 1950 (only 3 pages worth). They describe ugly buildings, ugly people but nothing to suggest to me the figurative transition you seek.
There are also references to post '9/11' and the actions, primarily militarily, that earn the figurative sense. gnovis.com