Depends on the type of bomb, the yield, and if it was an air burst or ground burst strike. Back in the cold war they used to say between 3 and 6 weeks but with modern nukes which have larger yields it's actually probably less time because they are fusion based, which don't produce as much radioactivity.

Just make sure to ignore the preppers, because they haven't actually got a clue. One of the things they always seem to stock is hunting equipment, so they're proposing to go hunt after a nuclear fallout event. Yeah they went won't long.

I think 2 or 3 weeks, you should wait for the government to tell you that it's safe though

What is the minimum safe time to shelter?

24 hours absolute minimum. 72 hours per most civil defence authorities. 14 days for a designed shelter in a fallout zone.

And after that, it depends on how much of society is left.

But you also have to think about the time the shelter is on standby, and that might be decades. You don't want by the time you enter the shelter to find out there is mold everywhere, the food is all expired and the fuel tank corroded and leaked.

Just until you die. So maybe a few decades.