I am not an Islamic studies expert, or a Muslim myself, but I'm pretty sure this does not differ much in Islam as in the Catholic faith (in a variant of which I've grown), for example, so here is my take on it.

* Regarding what the Quran actually says:
There are probably many passages that can be interpreted as referring to women's dress. They are probably all quite metaphoric/poetic and not very clear. They are written in classic Arabic, which makes matters of interpretation all the more variable... Call me a relativist, but there are probably many different ways to interpret it, going from a 'modest attitude' to the burqua (Taliban-style).

By the way, Muslim men also generally are told not to wear shorts and are supposed to grow a beard. Here interpretations vary as well...

If one searches the bible for long enough, one will certainly fine many references to how women should dress, just as poetic and metaphorical... Different versions of the bible will differ... The bible was also written in ancient languages or versions of languages, so translations/interpretations vary.

* Regarding the relations between culture, religion, and the State:
Some countries have adopted Islam as a state religion. They are usually the countries where the religious sayings are interpreted in their most conservative version. Correct my outsider's point of view, but it seems to me that in the USA, some states are also closer to organized religion than others, and it's also where the most conservative interpretations of religion are most frequent. All over the world, for a few centuries, if not millenia, the struggle between political powers and religious powers has been continuous. In general, when they get very close (with the religion on top), women don't get a very good deal or lots of options.

* Regarding Muslim women in non-Muslim countries who decide to abide by more traditional religious principle:
I'm not sure what I think about that, but I tend to think that, just like non-Muslim women (and men) by the way, it's not so much a matter of 'choice' as of internalizing what we feel is 'normal', 'good', what we've grown up around, what we take for granted as the right way to do things. Sure I 'choose' to dress up and wear a nice suit for a job interview, but honestly it would be unthinkable for me to do otherwise, just as it would be unthinkable for these young women to go to the beach wearing a tiny bikini. (Isn't extreme to show as much skin as "we" do to go swimming?)

* To answer the original question by Mr. Silver, my .02 cents (Canadian $):
Depending on their country, culture, education, tradition, family, desire to show affiliation to the above, etc., their mileage... er, coverage may vary.



Edited to add: I don't think there is such a thing as a written, ancestral version of the sharia.