As for the hypocrisy of the church in promoting nudity in art , eg the statue of David and countless other naked statues and pictures in the Vatican and other places , and then dressing the clergy and religious orders in some of the most ridiculous and impractical habits. Well, you be the judge!
In short, modesty is an attitude in your head and not necessarily related to what you are wearing or not wearing in the case of bikinis.
In the beginning Adam and Eve were naked yet felt no shame. After the fall they felt shame and covered their nakedness.In the TOB John Paul II notes pretty clearly notes they cover themselves on account of the shame;
This is the woman's shame with regard to the man, and also the man's with regard to the woman. This mutual shame obliges them to cover their own nakedness, to hide their own bodies, to remove from the man's sight what is the visible sign of femininity, and from the woman's sight what is the visible sign of masculinity. (TOB May 28th, 1980)This shame though does not (as you note) come from the body. Rather it's from the fear of what we might do to each other now that we are fallen and lust has entered the picture. We in a sense cover ourselves to protect ourselves from each other.
Modesty is a virtue that allows us to be excellent in relationship. It's about what we say, how we act and what we wear. Modesty is gracious. So of course it's important that we have the interior disposition, but their also needs to be an exterior manifestation. Have you ever watched TLC's What not to Wear? Many of the people on the show think they are classy dressers until the hosts set them straight. They have no idea that they are driving others crazy with their wardrobe because the others are being polite. There are others who dress poorly out of a kind of pride, and in the course of the show get humbled, and in getting humbled let others into their life.
No, clothes aren't everything, and I am certainly not advocating blowing large sums of money on a wardrobe (i've got most of my stuff from Thrift!) But I am saying that beauty is based on the truth, and that some clothes are objectively immodest. If a woman has modest thoughts but dresses in an objectively provocative fashion for mass, that's small consolation to the guy who has to focus hard not to fall for a temptation. It's the same thing on the beach or the office...
Most things and actions in life are neither good nor bad. But they can be bad because of bad intentions or because they are done inappropriately. And vice versa. Your own example of when and where you have or would wear a bikini is a good example.
The mere act of wearing a bikini is neither bad nor good in itself. But wearing one to Church would definitely be sinful.
As Jerry pointed out with his references, even between a husband and wife, sex could be sinful if it is engaged in solely for its own sack without regard for the purposes for which it exists.
So if you wear a bikini solely to flaunt your body, it is sinful.