What is the quickest way to kill a wither in minecraft!

The fastest way to kill a wither is to build an obsidian cage and summon it inside.

Post scriptum !Prepare yourself with good armor and milk buckets!

Important: I wrote this answer before noticing the question is about Bedrock Edition. The information below is valid for Java; please test in creative before trying to use on BE.

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A wither cheesing setup is easy and painless. You need a 3x3 formation of bedrock accessible from below. It's somewhat tricky to find such in the Nether ceiling (although there are tools for that) but you can skip the search - the End return portal provides one very conveniently.

Hollow out the area under the End Portal, leaving 2 blocks of space. Place 4 obsidian blocks in form of 'T' with the 'leg' of the T in the dead center of the portal (the line of three blocks 1 block "off". Build your wither flat - horizontal, with soulsand on the obsidian.

The wither will deal a little damage with the initial explosion (just enough so that a lot of baby chicks spawned from a ton of eggs, weakened with splash potion of poison will die dropping a bunch of wither roses) but beyond that it's quite powerless - slash it with a good sword and you'll kill it in some 20-30 seconds, without any danger.

Important: Double-check that the block with the wither's "legs" (the one soulsand block without a skull) is directly under the central column of the portal, otherwise there's a risk the wither may escape.

If you don't have access to the End yet, dig a long (100+ blocks) 2-wide, 2-tall tunnel with NO CAVES and no surface (or ocean bottom) nearby - not within good ~8 blocks from the tunnel. Spawn the wither at the end of the tunnel, then keep retreating, shooting it with a bow, as it progressively eats its way through the land widening the tunnel to fit in its chase after you. It's much less reliable and quite unsafe (especially if the wither does break through to access some cave, or worse, escapes to the surface), but it's the most reliable non-cheesing way of killing a wither.

ps. Regarding obsidian cages: Wither was spawned inside this obsidian cage.

This is the same cage a couple seconds later.

You could try spawning it at the top of the nether, it might not work. Since the top is bedrock, you could make a obsidian platform and hit the wither to keep it from moving out. Just to note: I haven’t actually tried this before, it is how I am planning to fight the wither. I don’t even know if you can spawn the wither in the nether. Edit: by top of the nether, I meant using the bedrock ceiling to suffocate the wither, not get on top and spawn it.