Definitely, it is Ok for a Christian woman to wear a bikini, in my opinion. The human body is beautiful and to be admired. False modesty or embarrassment about our bodies is a cultural relic of Middle Eastern desert cultures that really makes little sense. Look at the burkahs of sharia law countries now and you will see this embarrassment of the body taken to its extreme. Fear of bikinis is in the same catagory.
The body should be celebrated just as should be the mind and the heart and all the gifts of humanness. We are not Puritans, although clearly some on this site would like to see us revert to Puritanism or a christian form of sharia law. Fine if that's what you want, but not for me.
Of course, there is a time and a place for everything. The term is decorum. One should not wear a bikini to a formal dinner party or to sunday mass. But a bikini on a hot day at the beach, on a boat, swimming or in your back yard is perfectly appropriate in my book.
In fact I see nothing wrong with women going topless in those situations. I've spent time in villages where this was common and women breast fed in public and I thought it was the most natural, beautiful, and heathy thing in the world. In that atmosphere, the false cultural sexual baggage that western culture places on the female breast disappears and it is just physical beauty in the same sense as a leg, and arm or a face, with an appropriate function and lots of variety in form.
I'm reminded of how Jesus handled the cultural baggage of dietary laws in his day. He said that it is not what a man puts into his mouth that defiles him, but rather what come out of his mouth. I think it is the same with the human body. It is not the sight of a human body that defiles a person but rather the mental response...often culturally conditioned, that a man has to the sight. Cultures invented this embarrassment about the body and one can rid oneself of the false attitude by just chosing to do so.
Of course, being a physician, i see lots of bodies and so maybe have a more open minded view of this than more sheltered souls. Still, I think my view is sound. I had it before my training. If you look over most traditional societies, breasts are usually uncovered in warm climates, while the sexual organs are usually covered. This is natural. Breasts are not sexual organs and neither is skin. The area that should be modestly covered and reserved for the husband is indeed rather small.
So, I say, enjoy your bikinis. There are a lot more important issues to worry about! Like what comes out of our mouths :-)