Dropping is a move action [http://archive.wizards.com/default.asp?x=dnd/rg/20040706a]
Because it is freefalling and creatures who don't fly in a freefall only have their standard action.
"A creature can avoid damage from [a dropped] attack by making a DC 15 Reflex save." [HoB68]. It also states you could always dive bomb. Battle jump just gives a multiplier if you jump to or from above (or if they miss the DC15 reflex and you take your move action to drop).