I don't have a "bug-out bag", but my husband and I do have an "earthquake kit". It is the core/critical part of our camping gear, which lives in the back part of our SUV. It contains at least three gallons of potable water (more in summer), dehydrated food supplies for two weeks, small backpacking stove with fuel, camping pots/dishes/silverware kit, sanitary kit (soap, alcohol sanitizer, sponge, towels), a well-stocked first aid kit with a month's supply of any medicines either of us takes regularly, sleeping bags, a silver tarp (radiant heat barrier and signaling device), a tool kit, a trowel, a folding shovel, swiss army knife and larger hunting knife, a skein of rope, a ball of strong string, couple of other things.
The guns themselves, and spare magazines or speed loaders, are on us when we leave the house, so aren't in the kit itself. We need to put together a bag with ammunition and cleaning supplies that can be grabbed on the way out the door or left in the SUV.
The purpose of our emergency supplies isn't to have something in case civilization as a whole collapses, by the way; I figure that's both extremely unlikely and largely unsurvivable. But I lived in California for over 20 years until recently. I've lived through the Loma Prieta earthquake (7.1) that took down the San Francisco/Oakland Bay bridge and pieces of freeways, and have never forgotten how that was and how much worse it could have been.
In other parts of the country, maybe your emergency kit will be your "tornado kit" or your "hurricane kit" or something else. But IMHO *everyone* should have emergency supplies and be able to take care of themselves for a week or two with no help from any government agency whatsoever. You get extra points if you can take care of a few of your neighbors too.