If you are crazy rich you can have the same kind of air systems submarines use they are closed cycle needing only electric power to run. A small nuke would power one for 40 years much like out submarines have 40+ year reactor core lifetimes. The only waste product is CO2 which if you have a hydroponic grow set up could be used to feed plants closing the system. Water from waste recovered to same plants. Think space station or journey to Mars technology humans already perfected it. With billionaire money go fully closed cycle using space tech.
I love submarines because they’re sneaky. If a sub comes under attack, it can turn around and run away or hide.
An underground bunker can’t run or hide, and I don’t care how many high-tech gadgets it has. Once a bunker has been located, it’s a matter of time before it gets cracked open like an egg.