If you split bivvy bags into 2 types then it simplifies things:
Type 1 – Often no zips, hood with drawcord. Pretty much a waterproof sleeping bag cover.
Type 2 – Often has a zip closure, may have midge netting over the opening too. Often much bigger and boxier than type 1. Many will have thicker/more durable bottoms.
So, with type 1 a small part of your face is going to be showing (as fourbanger says you can kip on your front) so if it’s raining there’s a chance some water is going to get in with you. You’re also going to have to store kit ‘outside’ in drybags or bin liners. If I thought there was a chance of rain and I had a type 1 bag, I’d also take a tarp. You’ve also no protection from midges, etc unless you take a seperate net.
With a type 2 bag you can fully enclose yourself within it if it rains. Many also have enough space to fit a pack in there with you too and your sleeping mat will no doubt be in there with you also … something not all type 1 bags have space for. You could pretty much sleep out any amount of rain in a type 2 bag, even without a tarp.
Type 2’s tend to be more expensive as they’re often made from highly breathable materials (eVent, Goretex, etc) to help stop condensation forming when you’re sealed in side. Cheap bags from £20, good type 2 – skys the limit.