A bug out bag is.
Well a duffle, back pack (s), Pellican case or rubber maid container.
they are filled with items you will need if you need to leave the house for an emergency.
Riot, flood, mudslide, fire, earth quake, gas leak, chemical spill, or other problem where you need to leave the house in a hurry.
It is usually filled with some food, water, a water purifer, Medicine (needs to be rotated out but if you need a perscription it is in there), First aid kit, $ (if power goes out your ATM is useless), flash lights/ lantern, spare batteries, maybe a tent, firearm, ammo, blades. Enough for 3 days to a week for the whole family. Including Dog / cat or in your case Rabbit chow. with a bowl for them to use for water.
Depending on where you live, how many people you have, what your plan is (based on emergency), Where you are heading, and what the possible danger is is what you are going to carry in your bag.
When I lived on a top of a hill in southern CA every night on my way home I filled my gas tank and would toss my bag in the truck during fire season. That way all I needed to do was toss the dog in and get down the hill. Wild Fire was my only concern. As there were 2 ways down the hill. When I moved a mile away still on the same hill, I now had two horses to deal with and they were part of the plan was to ride them down with the dog. The bug out bag became saddlebags with the plan to ride the horses to my friends barn.