Bivys were popular years back when tents were bulky and heavy. You can now buy an light tent for just a pound or so heavier than a bivy. The tent is much more comfortable and definitly better in poor weather. A good bivy is about $200 and a good light tent about $300-$400. I have two bivies and three tents, and I mostly use the tents now. The basic bivy is 1# 6 oz and the tents are about 2# 7oz. A bivy is very different to sleep in- some people simply cannot tolerate the restricted space. By the time you add a small tarp to the bivy, you essentially are the same weight and bulk as a tent.

If I were you, I would look into 1-person light tents instead.