Salt water doesn't have anything in it to break down or react with fabric. Chlorinated water does. You should be able to swim in saltwater in anything that you can safely wear, sweat in, and machine wash. But if you want to swim in a pool you should choose things that are designed to be worn in pools - for instance, a women's racing swim suit or polo suit can have a pretty good binding effect. The Underworks binders also seem to be fine - at least I've never heard anything to indicate they have problems in any form of water.
As far as Ace bandages specifically, all I can say is that soggy Ace bandages are heavy and don't really do very much. And moving water can get under them and lift up the edges and make them roll, stretch, or slide in unpredictable ways. You might be better off just wearing your sports bra.
What I wore to swim this summer was swim trunks, an Underworks 998 T-shirt style binder, and a sun protection shirt (I wore mountain biking style, but who cares, as long as it's opaque and looks good) on top.
