I have been bivvying for years.
I don't have very modern / good kit, but I can cope with pretty adverse conditions.
I have a gore tex bivy bag, a decent sleeping bag, and I use a lot of bubble wrap.
The critical thing is the sleeping bag. I have a good one.
The outer layer (my gore tex bivvy) also helps tonnes if you are going to be exposed to the elements. If you can get out of the wind and rain it is nearly redundant, but I always use it to protect my sleeping bag from wear.
To insulate from the ground I lie on bubble wrap. I use a big bit from a bike packaging job on some bike someone sent me. I always manage to have enough without a problem. Getting more is easy everywhere. It weighs almost nothing.
In very cold conditions I wear my cold weather gear. Thermal leggings, thick dryish socks, down jacket and a woolly hat.
When zipped up into the bivvy bag in poor weather I drape a piece of fabric over the "breathing hole" of the bivvy bag, usually my shirt.
Often I just rely on my choice of sleeping spot and use the shelter it provides.
I think that is what I have learnt most. Where I sleep is more important than what I sleep in.
If you fancy a midwinter bivvying trip let me know, I have slept outdoors very comfortably in very very cold weather.