D.N.
When I was in HS, I had a bathing suit that was half black and half white. The white side would get see through when wet. you don't realize this when you buy it. My sister bought some material at Hanover Fabrics and sewed it into the suit. It worked really well and was not bulky. You should be able to go to a fabric store and ask for a material that will not go transparent when wet.