By large armies of trained soldiers who invariably suffered disproportionate casualties. Fortifications are very effective for this specific application.
The billionaire with a doomsday bunker probably has enough rations to outlast you. It's best not to wait until the doomsday bunker stage to do something about the situation.
That's true. However, the smarter(esque) billionaires built their doomsday prepper bunkers in NZ, AU, Hawaii, and probably elsewhere secret and far away from most civilization they want to avoid.