The word bandeau refers strictly to the top of the swimsuit. While most bathing suits have some style of shoulder straps, the traditional bandeau does not.
Sometimes it is also known as strapless or off shoulder swimsuit.
Imagine a skinny tube top, tie a cord around the front from top to bottom to gather it in the center and you have a working image of a bandeau. Some designs use a center ring or keyhole to achieve the same effect.