Just to clarify: There are two kinds of bivy.

One is a stand-alone bivy which is waterproof. It may have problems with condensation and certainly it will be difficult to get into and out of when it's raining without letting water inside. They are used primarily by mountaineers who will be out only one night but need to be able to curl up in a small space.

The other type of bivy is a durable water repellent (not waterproof) sleeping bag cover which protects your sleeping bag from splash, drip, and windblown rain/snow when you're sleeping under a tarp. Being more breathable than the stand-alone type, it's less apt to have condensation inside. It's also a lot lighter than the stand-alone type. It usually has a bug net over the face and a waterproof underside so can substitute for the ground sheet and bug net needed with just a tarp.

With a large enough tarp that you can stake close to the ground in rain storms, you really don't need the bivy. However, you do need a ground sheet and (in bug season) a bug net if you don't have a bivy.