In which cultures?

There is iconographic material from the Minoan period on Crete where exposed breasts are portrayed, both statuettes and frescoes of bullfighting. Of course, the question remains whether that only happened in a ritual context or also commonly in daily life.

I can't do it right now, but I would search Roman writers and after that the Church fathers for their views on female nudity, to detect whether there was a notable surge of inducing shame in people for being naked in public. Caveat: it's not because they rant against public female nudity that that was the morality of the times; it might just as well mean that the practice was common and they were rallying against it from their exceptional religious sensibility. Do keep in mind that there can be considerable regional variation in accepted practices, and do not assume there is a linear trend progressing to a certain point either.

As a follow up or further question, did this have more to do with female ideals of beauty or with come practical, functional aspect of society?

In almost all cultures and certainly most cultures that wrote things down pre-feminism, women's sexuality is seen as a finite resource that must be guarded.

Women traditionally had trouble getting married if they weren't virgins and could often be killed if they had sex with someone their family didnt okay. Now we associate honor killings with Muslim countries, but it was the norm just about everywhere in one way or another until very recently.

Men on the other hand were encouraged to sow their wild oats. There were some exceptions to this, but it was the overwhelming norm. So thus while men could show off their muscles with no dishonor, women typically could not. I think this is the genesis of the taboo.