How do I get the cleaning bucket?

Usually sunny will warn you about selling important items, and you can usually cancel the sell if you did not tap away.

If you mean the bucket that generates cleaning items, that's going to be quite hard if you accidentally sold it. You can only get them on every other level up (I think the brown chest gives them out) and occasionally during events if you bought enough decorations.

If it was a very high level bucket, you may have a hard time progressing. It wouldn't hurt to try contacting sunny house support directly and see if they can give you a new one. If they can't reimburse you and you literally don't have any other cleaning buckets and can't advance the game (due to quests requiring cleaning items) you may want to consider starting a new game.