You’ll find that opinions on setups are as personal as bike choice!
It’s worth checking out the Bear Bones Bikepacking forum. EDIT: beaten to it by Scotroutes
Personally, for bivvying i’ve tried a few bags and have settled on an Alpkit Hunka XL which gives me freedom to move about. I use the mat outside the bivvy bag.
I use down quilts (Enlightened Equipment and Cumulus) rather than sleeping bags and sleep as I would at home in a bed! Arms in or out depending on how hot I am.
Whilst bivvying is great for that “rugged, outsdoorsy” image, most of the time I use a Lunar Solo tarp tent to protect from the elements, bugs etc.
I have a Neoair X lite mat and use either a Bear Bones meths stove or MSR Pocket Rocket gas stove with Alpkit Ti cookware.