Good news: creating a bubble that size seems emminently possible using current-day technology.
Bad news: promptly vapourising and displacing that much water, and the secondary effects of whatever means you use to do so, will result in an Extremely Hostile environment for aircraft.
You're trying to move something like 540 million tonnes of seawater out of a 1km deep volume faster than the entire ocean can flow back in. Canute got nothing on you.
Working out how quickly that cavity will collapse is hard, and alas this answer will be incomplete because I can't actually calculate it for you. Instead, lets look at the amount of energy required to excavate the cavity, and the effects it will have on the local environment.
How much energy? Well, for similar reasons, I can't give you anything other than very broad approximations, but it looks like you'll need 30-100 megatonnes TNT equivalent to form a big enough hole. I've got these numbers from a presentation on asteroid impacts in water. The authors didn't consider your specific scenario for some reason, but you'll see (on page 37) a brief mention of a 100m asteroid striking deep water, 66MT equivalent blast, 1.2km deep transient crater. That's a good ballpark figure. (The Operation Wigwam test that Separatrix references uses a ~30kt warhead to develop a ~100m bubble. A 1000m bubble has 1000 times the volume, and 30MT is about a thousand times more powerful a bomb, so it seems about right)
Now, quite a lot of that blast energy will go into vapourising seawater. The expansion of that steam will help push the surrounding water out of the way. Beacuse you want your cavity to reach the surface, a good deal of that steam will escape upwards. This is important, because you have just generated a (approximately) a cubic kilometre of steam which is going to rise up rapidly and mix turbulently with the atmosphere. This will result in hurricane force winds, which in the vicinity of the cavity will be boiling, wet, hurricane force winds (if you look at the asteroid impact presentation, it suggests hurricane force winds withing 22km, and temperatures >100C with 5km, which again, are good ballpark figures). Oh, and also radioactive. Mustn't forget that. This is not an aircraft friendly environment. You probably won't get a nuclear fireball forming, but from the point of view of your aircraft it won't really matter. Sure, these conditions won't persist, but they'll last at least as long as the cavity does, so you'll have to deal with them if you want to fly through the hole.
Finally, when the cavity collapses, you'll get all sorts of really interesting hydrodynamic effects. You'll get a jet of water formed that could reach a few kilometres into the sky. The formation of this jet will cause an intense pressure wave at the bottom of the cavity. Between this and the nuclear blast you've used to create the cavity in the first place, the chance of anything immediately underneath the cavity surviving are extremely slim. I hope that door and the thing it protects are very robust. Incidentally, can you rely on the door opening fast enough to fly in, and close fast enough such that everything doesn't get smooshed?
So, how quickly will the cavity collapse? It doesn't matter. Nothing will survive its flight into it.