Tribal women in Africa, South America and Papua New Guinea have gone around with bare breasts for countless generations. When Christian missionaries arrived they convinced the women to cover their breasts. What arguments did they use to achieve this? I see nothing in the Bible about God commanding women to cover their breasts.
No, there are no explicit instructions in the Bible to not have bare breasts. Biblical references to modesty are interpreted differently given a particular time and place -- similarly with interpretations of 'nakedness.' There is no explicit verse covering the topic, Christians must infer instructions of modesty on their own. This has been accomplished in a wide variety of ways throughout history. Contemporary women's clothing would be have been considered horrifyingly indecent centuries ago, but they are commonly worn by Christians today.
The only specific article of clothing that a small minority of Christians adhere to is St. Paul's instruction for women to cover their heads (1 Corinthians 11:1-16). Many contemporary Christians interpret that instruction to be specific to the congregation he was speaking to due to the context of their time and place (same with the references to gold, pearls, and remaining silent).
First Timothy states:
Likewise, I want women to adorn themselves with proper clothing, modestly and discreetly, not with braided hair and gold or pearls or costly garments
1 Timothy 2:9 (NASB)
The following 2 verses put together could also help:
but I say to you that everyone who looks at a woman with lust for her has already committed adultery with her in his heart.
Matthew 5:28 (NASB)
It is good not to eat meat or to drink wine, or to do anything by which your brother stumbles.
Romans 14:21 (NASB)
And let's not forget that God made clothes for Adam and Eve after the fall for a purpose:
The Lord God made garments of skin for Adam and his wife, and clothed them
Genesis 3:21 (NASB)
First of all, I would hope that we can all agree that it's a commandment to not walk around naked. Hence why God made Adam and Eve coats of skins to cover their nakedness after they had eaten the fruit and were no longer innocent.
The only scripture I know of specifically referring to covering the breasts of a woman as covering her nakedness is in Ezekiel (actually referring to Jerusalem):
7 I have caused thee to multiply as the bud of the field, and thou hast increased and waxen great, and thou art come to excellent ornaments: thy breasts are fashioned, and thine hair is grown, whereas thou wast naked and bare.
8 Now when I passed by thee, and looked upon thee, behold, thy time was the time of love; and I spread my skirt over thee, and covered thy nakedness: (Ezekiel 16:7-8)
Biblically, women were considered naked not only when they were undressed, but also when they were not properly dressed. A woman was not considered properly dressed if she was showing anything that might arouse sexual desire in a man. Walking around topless would certainly qualify as being naked.