The Church doesn't have a standing list of what styles of swimsuit are appropriate, but General Authorities have given specific counsel to avoid clothing that doesn't cover the stomach or that is low cut. Years ago, the Church did have a specific guideline to not wear "two-piece" swimsuits, meaning bikinis.
One-piece swimsuits certainly aren't the only style of modest swimsuit, and all one-piece swimsuits aren't necessarily modest (you can buy plenty of one-piece suits that have cutouts or dip really low in the front, for example), but they're one style that tends to cover more skin than some other styles.