Bivvy / Bivy is really known as a Bivouac sack, bivy sack or bivy bag, an very lightweight alternate shelter to the usual tent systems.
Fishermen and women use these in a half dome design to keep the cold and wet weather out. They make a great shelter for overnight fishing trips and a bivvy can be turned quite easy to avoid the wind direction.
A Bivvy can cost as little as £20+ for a budget one and as much as £100+ for a quality one. The bivvy design is very similar to a normal tent but is structured to have a big opening to fish from.