I know there won't be a definitive answer because breasts are not considered taboo in all cultures, but is there a point in history where maybe a pattern emerged amongst developed countries to start covering breasts?
Seems as though penis and vagina are almost always covered no matter the culture, but there are a lot of tribes that just view breasts as a food source for children and have no taboo attached.
Edit: thank you for all of the great responses!
As /u/sd42790 said, this is more of an anthropological question than a historical question, but luckily, I'm an anthropologist. ;)
There is no real way to answer this definitively, as the degree to which bare female breasts are made taboo as well as the degree to which breasts are sexualized in general is going to vary greatly by culture and across time.
What we do know is that there is a class of artifacts from as far back as the paleolithic era in Europe called "Venus Figurines", which depict nude adult female bodies with enlarged sexual organs and/or breasts. They are over 20,000 years old.
There are many opposing opinions on exactly what Venus figurines represent (see linked papers below), but most interpretations are "hyper sexualized" in some way . . . most commonly as "fertility symbols", but even as ancient pornography.
There have also been feminist interpretations of these figures as being self images of the artist herself. [Note, the paper I linked to is NSFW because they contain nude photographs used to compare body proportions to Venus figurines.]
TL;DR: Old Stone Age Venus figurines are mysterious, usually depict exaggerated breasts, and are the earliest surviving depictions of sexualized female bodies of which I am aware.
Other sources:
http://www.hindawi.com/journals/janthro/2011/569120/
http://digitalcommons.wou.edu/cgi/viewcontent.cgi?article=1051&context=pure
The answer to your question is likely prehistoric. You may consider cross-posting to r/askanthropology as well.