The problem with option #1 is you can be as good as you like but you are still screwed if some other asshole pushes the button. At least with option #2, you have some control over your your survival.
Plus, these options are not mutually exclusive. You can do your best to ensure a just, peaceable world while still digging a really big bunker.
You are right, of course. If I had the money I would absolutely build a bunker, even if it was just as an entertaining project.
The fact that we hear about Zuck and Altmann being the ones prepping or building bunkers could reflect that they are the "bad" elite, not invested in the future of the planet in the same way that Gates and his ilk are. Or alternatively, it could just be that old people don't find the idea of a survival shelter nearly as interesting as the younger generation.
Those who are valuable today are not likely to be the ones valuable post-doomsday. I’d imagine the bunkered billionaires plan to use a private mercenary force to assist in recruiting whatever useful post-doomsday talent is left afterwards.
The one thing I genuinely wonder is what odds each billionaires gives their private mercenary force for not usurping the “throne” from them after an apocalypse.
Option 2: Dig a big hole to live in while the poors eat each other