Kit,
To go Bivvying (is this the verb to bivvy?)
You need:
A Bivvi bag – Alpkit Hunka or Ex-army seem to be fine
Food & Water
Non luxury optional extras:
Sleeping bag – Smaller the better
Mat – Smaller the better
Luxury optional extras:
Small tarp to keep rail off face (depending bag style)
Stove (if you want hot food or tea)
Change of clothes to sleep in
The Bivvy book chap seems to think that a crappy light sleeping bag and more clothes is a better option than a super duper sleeping bag as you can put the clothes on to sleep in and use them if it's cold while out. Whereas a sleeping bag can only be used to sleep in. There seems to be method in the madness.
Also why take a stove? If your only overnighting a packet of Custard Creams will see you through