It might reduce the EMP enough if it was deeply buried, but it would depend on what the bunker was made out of, and other considerations. Very deeply buried bunkers would pick up less direct EMP, but the EMP could still enter via cables connected to it, if not protected. If it was a small purpose built bunker made out of steel plate, or a steel cylinder, perhaps lowered into the ground by a crane, then some reduction in EMP would be likely. But the trouble would be that the doors would only normally have rubber seals, not copper strips to form R.F. seals around them. Then the bunker would have openings for air intakes and other services.

With buried shipping containers used as bunkers, as they come, the floors are made of wood just clipped to C shaped steel beams spaced a bit more than every foot, so you wouldn't have any complete big metal box to form a Faraday Cage, plus even if the floor did have extra continuous steel plates welded on, the big double doors would be even worse for EMP penetration. Never bury a shipping container without extra reinforcing and waterproofing anyway, as they are only strong at the corners and the roofs and walls can collapse when buried, plus they are not watertight. I certainly don't recommend burying them, though some people do.

With reinforced concrete you wouldn't have a Faraday Cage either, though if the rebar was the usual closely spaced double face type forming thousands of rectangles, it might attenuate the EMP penetration very slightly, though probably nothing of any significance to be of use. Our big reinforced concrete bunkers, often at least 50 feet below ground, usually still had one or more special rooms totally enclosed with metal, and with the copper strip seals all around the metal doors. Galvanised steel sheet was commonly used, as it isn't a case of thicker metal cutting the EMP down more than thin metal.

Home made Faraday Cages don't need to be fancy or expensive. 2 tins, each lined with thick cardboard, one inside the other, each with their metal lids firmly on and on unpainted metal where they clip on. Ideally, once the electronics is inside the inner tin, both tins should have aluminium tape wrapped all around where the metal lids go on too. Leave any batteries to operate the radio or whatever, outside of the cages, in case they should leak. I'd put them in a little plastic bag taped to the outer tin. Some folks use metal trash cans for the outer tin. Being galvanised, they are resistant to rusting, plus the lids make a good contact through the galvanising zinc coating, unlike paint, which would ideally need to be sanded off. Best to use new trash cans or tins in very good condition, so the lids fit and connect well.

On our RAF communication bunkers it was considered necessary to regularly clean the copper strips around the inner doors that go after the steel outer blast doors, using isopropyl alcohol. Tests proved that even a bit of tarnishing or grease on the copper seals could considerably effect their integrity against RF leakage. It was that critical. Even You Tube videos using test gear show that adding the aluminium tape to the lids of home made Faraday Cages is worthwhile for further reduction in EMP penetration. Military bunkers have specially made protective filters and devices in them,such as high speed spark gaps, to protect the internal equipment from EMP picked up via the incoming cables. EMP is far faster than lightning, so ordinary protection against that is not good enough.