Shockbound
Smash Apprentice
It should become very clear when the opponent intends to hit you again. Bucket stalling on the way down moments before they would normally hit screws up people's timing immensely. It's also much easier to act out of than a double jump, since you can D-Air right there to smack 'em during their endlag. Doing this also lets you keep your double jump to further act upon that punish.
Bucket stall should really only be used immediately after hitstun to avoid immediately being sent over the horizontal blastzone. It will stop you faster than a double jump. If you're going off the top, bucket is going to be of much more use to you on the way down. When offstage horizontally, the odds of the opponent trying to juggle you from there are slim.
Fastfall N-Air, D-Air, and F-Air (flub) are all decent options for coming down, but you have a lot of options from bucket stall that can interrupt your trajectory and make your opponent have to think a lot more about where you're going.
Bucket stall should really only be used immediately after hitstun to avoid immediately being sent over the horizontal blastzone. It will stop you faster than a double jump. If you're going off the top, bucket is going to be of much more use to you on the way down. When offstage horizontally, the odds of the opponent trying to juggle you from there are slim.
Fastfall N-Air, D-Air, and F-Air (flub) are all decent options for coming down, but you have a lot of options from bucket stall that can interrupt your trajectory and make your opponent have to think a lot more about where you're going.