You know how sometimes when it rains you get a little and the next street gets a hosing? Radiation from a bomb is like that.

The initial radiation cannot be avoided but, by definition, does not last long. Fallout is subject to the vagaries of the wind and weather, perhaps you have none a mile away upwind from GZ, perhaps it 'rains out' and you have a lot just on you an hour later.

Fine particles go almost to space and get distributed around the world for years being diluted as they go, A ground burst also kicks up pebbles on which the radiation 'condenses' that fall out of the sky quite close and quickly. And there is everything in between. Air bursts are the most likely scenario as they do more damage (energy is not wasted digging a hole in the ground) and the fallout is minimal compared to a ground burst. You may not need to shelter for a "very extended period" probably just a couple of hours.

How do you know what you have without measuring your surroundings.

We have already experienced a nuclear war and many, many survived, even close to GZ.

You are actually very likely to survive a nuclear strike and the subsequent radiation