The New York Times jobs section links through to the their international opportunities. There, when filtering on "Russian Federation" you can find a direct link to this job advert which reads, in full:
Vladimir Putin’s Russia remains one of the biggest stories in the world.
It sends out hit squads armed with nerve agents against its enemies, most ...
I couldn't find any evidence that Putin was hiding in a bunker for a significant amount of time in 2020. As it seems, most of the rumors come from the photos of his apparently windowless conference room in Novo-Ogaryovo.
The earliest reference to the "bunker" I could find was published on d3.ru in 2015: Is Putin in the Bunker?:
Путин в бункере?