A peplum is a little ruffle on the bottom edge of a short jacket that stops at the waist. It may stick out a little, especially at the back. The fashion comes and goes, but most people think that a woman who is wearing a dress or suit that has a peplum waist is trying to look nice and sort of dressed up.
A bandeau top on a bikini is one that goes straight across the breasts and around the chest without straps to hold it up. It’s not sewn into a particular shape; the breasts give it its shape. My experience is that a majority of men don’t object to seeing an attractive woman wearing one of these. At all.
Sounds like a tube top to me. Guys don’t like those? Who knew.