No duck and cover
My only school remembrances of the atomic bomb threat was during some perceived crisis my school had something similar to a fire drill that was related to evacuation instead of fire.
They also issued us dog tags to assist in IDing our charred remains, I suppose. That one stuck with me.
I don't remember any duck and cover drills but I am sure that the various States had different approaches.
National Civil Defense was never more than recommendations per my recollection