I currently live in a rental, but going to be moving to a new place soon, within the next year or so, that is already prepped. Right now I have several BOB in the various locations that I am frequently in. I have two in my apartment, for me and my girlfriend, located in the closet right beside the door. I got hiking rucksacks, the fkind that fit your body like a glove, and filled each of them with everything that we would need to survive for up to a week. Mine's kind of heavy, weighing in at 100 pds, but I'm used to carrying weight like that and did it for years in the military so it's no big deal. My GF's is lighter, hitting about 50 pds. But between the two we have food, clothing, survival gear, weapons and ammunition ready to go on a moments notice.
I also have one in each of our vehicles. No where near as large as the ones in the apartment, but enough to see us through at least 72 hours.
Hope this helps. I've been prepping in a rental one bedroom apartment forever so if you have any question feel free to ask.