Wow,
@MV , that was one hungry bunny! Or could it have been a groundhog? The rose will probably be able to produce new growth from its leaf axils, but I suggest you surround the bush with a tube of fence wire up to the height that a rabbit or groundhog can reach, and bury the base of the wire in the ground so they can't get under it. I recommend using fence wire with oblong, not square, openings so that snakes won't get stuck going through the holes.