You can store your bitcoin on paper and put it in a safe or even carry it around with you.

The effected area of an emp is at most an area the size of a couple of states.

"The internet" would keep right on running all over the world and in most of the United States as well.

The bitcoin miners are not in the U.S.

This would not be a long term situation in the whole country and that is the bogus part of all this. There would be an effected area surrounded by a larger area that was not effected. You would make it to civilization again and you would use your bitcoin again.

There definitely would be looters and mobs. They would be looking for valuable stuff, silver , gold , jewelry, etc.

There could be gangs or even soldiers shaking people down at checkpoints looking for valuables.