Mat 6:28 And why are you anxious about clothing? Consider the lilies of the field, how they grow: they neither toil nor spin, yet I tell you, even Solomon in all his glory was not arrayed like one of these.
Modesty is taught in scripture, and as it is taught there it is an important lesson for both men and women. The sort of modesty we find in the bible, however, has nothing to do with covering skin or sexuality of any sort. Rather, biblical modesty is synonymous with simplicity, humility, and having the right priorities.
(1Ti 2:8-10) I desire then that in every place the men should pray, lifting holy hands without anger or quarreling; likewise also that women should adorn themselves in respectable apparel, with modesty and self-control, not with braided hair and gold or pearls or costly attire, but with what is proper for women who profess godliness--with good works.
(1Pe 3:3-4) Do not let your adorning be external--the braiding of hair and the putting on of gold jewelry, or the clothing you wear-- but let your adorning be the hidden person of the heart with the imperishable beauty of a gentle and quiet spirit, which in God's sight is very precious.
I see this as an admonition to Christians to resist the temptation to be obsessed with the latest fashions and the temptation to put all our resources into maintaining a competitive appearance. It is natural to want to be beautiful, and admired, but the most important adornment for a Christian is our heart of love and service and the good works which flow from it.
Matthew Henry says, "Those that profess godliness should, in their dress, as well as other things, act as becomes their profession; instead of laying out their money on fine clothes, they must lay it out in works of piety and charity, which are properly called good works."
A practical example of this teaching would be the emphasis we Christians sometimes put on appearance in our worship services- do we require that worshipers dress expensively to fit in among us? Do we have a tacit dress code that cannot be met by those with limited resources? Do we care more about how nicely we are dressed for church, or how nicely others can see Christ in our actions when we're there? Do we accept all visitors to our fellowship as they are, endeavoring to see them as God sees them, as people with hearts, souls, minds, hopes, and pain of their own?
Barnes says, "The word here rendered “modest” (κόσμιος kosmios), properly relates to ornament, or decoration, and means that which is “well-ordered, decorous, becoming.” It does not, properly, mean modest in the sense of being opposed to that which is immodest, or which tends to excite improper passions and desires, but that which is becoming or appropriate."
(Jas 2:2-4) For if a man wearing a gold ring and fine clothing comes into your assembly, and a poor man in shabby clothing also comes in, and if you pay attention to the one who wears the fine clothing and say, "You sit here in a good place," while you say to the poor man, "You stand over there," or, "Sit down at my feet," have you not then made distinctions among yourselves and become judges with evil thoughts?
Also, dressing in such a way as to be situationally appropriate, simple, and pleasant without demanding a spotlight is an art form that we all, men and women, should attempt to practice. This has less to do with sexiness or coverage, and more to do with cultural context, practicality, and intentional simplicity, in my opinion. And, simple needn't be drab; it's more the antithesis of gaudy, extravagant, or garish. A two piece swimsuit can well fit into this paradigm at the beach, but the most covering, sexless swimsuit would not be the best choice for worship or school or a funeral, as the loveliest church dress would probably be inappropriate while working in the food bank or weeding the garden.