In many, perhaps even most, disasters bugging out may not be necessary or prudent; in these cases people should plan on sheltering-in-place or bugging in. Bugging in may be sheltering where you already are, or going to your bug in location (BIL), typically your home. There are many advantages to bugging in, the greatest of these being that you don't have to carry all the necessities for survival on your back. When bugging in, you must plan/provide for your basic needs (food, water, and shelter) without counting on external supports like electricity and running water or modern conveniences like flushing toilets and microwaves. Even given these limitations, it should be relatively simple for most people to prepare for a bug-in lasting 3 days, or longer.
Food for bugging in should be chosen with a number of factors in mind: long shelf-life, balanced nutrition, and ease of preparation. It should also be food that you (and your family) are willing to eat.
Food storage items such as rice, beans, canned goods, and the like are a great place to start when food-planning for bugging in. A good way to think about, and accumulate, food for bugging in is to think about shelf-stable foods that you already buy in your weekly shopping, and just get a little bit extra every time you go to the market. Having some variety and personal favorites mixed in with the food-supply is a good thing, as it will help maintain morale and possibly avoid/reduce stress and arguments in already difficult times.
It's not a bad idea to supplement your bug-in food with some MREs (Meals Ready to Eat), HDRs (Humanitarian Daily Rations), emergency ration bars (like Mainstay or MayDay bar), or GORP (Good Old Raisins and Peanuts: food that doesn't need any cooking or preparation at all, and provides reasonable amounts of calories from fat and protein.
A camp stove that will run when the power goes out is important if you plan to be doing any cooking. Make sure to do your cooking in a place with adequate ventilation if your stove is not rated for indoor use.
Water storage is probably the most important, and least-often provided for, emergency supply. When bugging in, you should plan on at least 1 gallon, per person, per day.
Rinsed out 2-liter soda bottles because they're tough, manageable, and free. A rule of thumb is 3 bottles per day for each person, which works out to just over 1.5 gallons per person. These bottles can be stored anywhere around the house, and probably should be changed out on a 6-12 month basis (although they may be safe for longer, why bother, it's both free and easy to refill the bottles).
Do not reuse plastic milk or juice jugs as they contain bacteria that may contaminate your water. Also the plastic used in milk jugs deteriorates after about 1 year meaning that your water storage could become an indoor flooding problem. It also is recommended to store your water in a dark cool place and do not store plastic containers directly on concrete. There is concern that concrete, especially warm concrete will react with the plastic and leach chemicals into the water and degrade the plastic.
It might be prudent to acquire a water filter, such as a Berkey type. Then you can filter whatever water you can find, and ensure that you always have enough. The Royal Berkey, for example, with the black filters, provides 3.5 gallons of water per hour, filtered to 99.99999% purity. This is assuming new filters and relatively clear water. Filters also have limitations. Even the Berkey filter cannot guarantee filtration of certain contaminants such as the 4-methylcyclohexane methanol spill in West Virginia (Jan 9, 2014) or salinated (salty) water. It is best to get the cleanest source possible. Collection could come from rain water collection, a pool, spa, or condensation in a solar still. You may want to knowledge of other filtering and purifying methods like a home made gravel, sand and charcoal filter, boiling, distilling, solar disinfection (SODIS) method, or using chemicals such as using bleach or iodine as backups. Combinations of these methods and the knowledge on how to do them could be helpful if you don't have a filter or want to pre-filter water.
When bugging in, shelter may seem like less of a concern...and it is...but in many regions, we take the heat in our homes for granted, and this can become a problem in a short time once the power goes out.
An indoor-use rated heater is highly recommended so as to avoid carbon monoxide poisoning that is a risk with some heating schemes that some people try during disasters, like using charcoal grills inside. This heater uses a propane tank from a gas grill; if you have 2 tanks, then one will always be full, and you will never run out during a cookout (or an emergency).
An alternative, or additional, path for filling the shelter-gaps left by your home when the heat goes off is just to dress warmer. Fleece and wool on your extremities (head/hands/feet) and in the form of sweaters and long underwear will go a long way to restoring your comfort, and preventing you from burning through too much of your bug-in food calories just keeping warm.
One might also wish to consider some basic level of weapons for the bug in location. For example, a shotgun can be a powerful deterrent to people wishing to scrounge through your home, while you are still living in it. However, know your local laws regarding weapons and use of force for self-defense.
Besides the basics of food/water/shelter, there are some other things that will help make bugging in more comfortable and manageable.
Paper/plastic products that can be thrown out rather than require water-intensive washing are a plus. Plan on enough toilet paper (1 roll per day is more than enough unless your family is huge). Antibacterial soap and wipes are great for cleaning hands and bodies when baths & showers are a thing of the past, and bleach can be used, when diluted with water, as a hand dip, surface cleaner, water purifier, and general disinfectant. Light from multiple sources is a good thing: lanterns, candles, flashlights and glow sticks all meet different but useful needs in emergencies. Matches and lighters in multiple locations and greater supply than you would think are also a great thing to have. Duct tape (Gorilla tape, pictured above, is worth getting) is useful for lots of things in both daily life and in an emergency, so why not include a roll.
There are lots of portable radios available that work without being plugged in, and without batteries, running off of power generated by a hand-crank dynamo. These are useful for keeping up to date with local/regional/national events in, and out, of a disaster zone. Some of these dynamo radios even allow charging of your cell phone through the hand-crank.
Make sure to have plenty of batteries for everything in your home, and especially everything in your bug-in plan, because without them, your gadgets are nothing more than paperweights.
Remember to keep some forms of entertainment around that you can use to keep people from stressing out.