Options exist with no expiration date, but they are not commonly traded. There's nothing in principle unusual about them, at least not more so than most other derivatives.
I mean a bursting bubble is what? A C-Suite pulling the valve shut or a company going under? It seems like the bubble has burst already then when Zuckerberg and Altman started decrying it earlier in the week. Now we just wait for all the smaller companies to either fold. For the larger companies the bubble will probably deflate slowly rather than burst.
There are no market indicators if the actual burst is at the whim of a human. Being that Meta can probably bleed for a while before seeing real losses after a burst. All they have to do is be the first one to stop growing while the bubble deflates.
A traditional bubble burst is when there is a major sector-wide selloff of an overinflated asset. When there is a race to not be one of the suckers left holding the bag.
"The market can stay irrational longer than you can stay solvent." -- John Maynard Keynes
Predicting when a bubble is going to burst is close to impossible.