I think you need to decide exactly what you want here.
A hammock will keep you off the ground, and if properly insulated, warm, but you have to have somewhere to hang it, and it won't keep you dry. So you'd need a basha or tarp or similar cover if it rains.
A bivvy bag will keep you slightly warmer and will definitely keep you dry, but won't keep you off the ground if the ground is unsuitable for sleeping on. (Think of a bivvy as a waterproof sleeping bag outer layer).
If you're going to be camping out, and you know it won't rain, or at least it won't rain heavily, then you can just as easily replace a bivvy bag with a cheap tarpaulin, which you can double over yourself for showers. However, if its going to rain at all, I always tend to prefer to take a bivvy bag AND a basha - if nothing else it keeps the rain off your face which you can only do in a bivvy if you seal yourself inside (which I find keeps me awake) and it gives you a bigger dry area to store kit in. I only carry a hammock if I know its going to be dry and there's a nice bit of forest to kip in - I've never quite got the technique for sleeping in a hammock right you see (being 6'5 doesn't help matters!)
