Not to be the last word by any means, but I tend to associate "bandeau" first with tops that don't extend above the
-- Edit, underarm, all the same right?
level. Wikipedia claims that "bandeau" traditionally doesn't include any straps -- In practice though, it seems more like the rule only refers to shoulder
Some places call these "criss cross tops" (Although that is not limited to tops of a short length. Full coverage blouses can be marked criss-cross when they include showy lines around the bust, too.) Some places choose to say "criss cross bra tops." I think that's perhaps more explanatory... But it doesn't roll off the tongue when you want to be short and sweet -- like the outfit.
My suspicion: There is no hard and fast rule, but as with women's sizing: So many local terms (and sales pitches).
Oh, but I did find pretty pictures along the way!