Bat dropping (sometimes abbreviated as BD) is a technique used primarily in the Home-Run Contest minigame to rack up very high damage on Sandbag. It is the act of dropping the bat over Sandbag, then hitting the bag with a move that does not send Sandbag flying, usually a meteor smash to hit the bag back into the ground, or some weak attack that negates the knockback of the bat drop.
Captain Falcon or Ganondorf's bat dropping technique is a classic example: they jump over the Sandbag, drop the bat, and then hit it with a down aerial. The bat knocks the bag up in midair and the spike immediately hits Sandbag back down; thus, Sandbag doesn't move. The bat should bounce off Sandbag, so one can jump and catch it again.
Not all characters have to use down aerial; examples are Mario's forward aerial, Yoshi's forward aerial, and Falco's up aerial. The timing for every character is different because of varying falling speed, attack speed, and jumping height.