How do I make a pickaxe that can break bedrock?

You can use the special can_place_on and can_destroy tags for MCBE.

/give @s minecraft:diamond_pickaxe 1 0 {"minecraft:can_destroy":{"blocks":["bedrock"]}}

but there's still a problem, because bedrock can't be broken, because that's the whole point, it's a barrier to stop you falling into the void! So even with a can_destroy tag for bedrock, you can swing your pickaxe at it as much as you want, but that bedrock isn't going to break.

You could retexture a different block to look like bedrock, but that's an entirely different mechanic for an entirely different post. Check out some info on add-ons for more info.

You would use a command to a) make bedrock breakable, since bedrock cannot be broken (requires significant command knowledge), and b) to give yourself a pick which can break bedrock (significantly less command knowledge required). However, this would most likely allow players to dig out of the world (bad thing). Xboxes are not good for modding, as the only NBT tags are the can_place and can_destroy tags. If you're in Adventure mode, and you managed to make bedrock breakable, use the following command:

/give @s minecraft:diamond_pickaxe 1 0 {"minecraft:can_destroy":{"blocks":["bedrock"]}}