You don't need anything under there. Just be sure to use a tightly woven tape or the boning will escape and possibly head into your drawers. Not that that's ever happened to me. (OK, it has. Not fun!)

It depends on the corset cover. I don't wear one with my velvet or red and black bustle dresses, but the wool dress was lightweight enough that I used a corset cover. Fortunately I had one made for that corset from my summer bustle dress. It can be made last and just be a sleeveless version of your bustle bodice. A lower neck on it is nice too...