Staying safe from fallout is about keeping radioactive dust/ash off of you which can, for the most part, simply be brushed or washed off, it's not about radiation itself which you cannot get away from. The whole idea is to minimize the amount of radiation absorbed by ensuring that you are not covered in radioactive materials.Everything I have heard, read or seen is "bug out quickly if possible." Compound that with fallout and you may be better in your house if it is relatively airtight (assuming no damage from the initial blast) and you have 8 or 10 feet of space between you and the outside. Fallout and radioisotopes tend to "stick" to stuff. If you are outside you no longer have that "bubble" around you and you hopefully are in anti-contamination clothing that is removable and fallout doesn't stick to as easily (with respirators of course.) If you are exposed, no scrubbing (thank movies for that myth) all you will do is abrade the skin and contaminate yourself further. All this of course is moot depending if the weapon was fission, fusion, yield and what designed for. A fusion bomb encased in cobalt (whose to say their are non in inventory) are the worst, even with an airspace of 10 feet Cobalt 60 is so radioactive game over. Fission airbursts are "cleanest" groundbursts with fusion weapons the dirtiest (neutron activation of soil and buildings.)
So is prepping a waste of time and money? Hence the debate.