Do the animation of the position and opacity of your first drop, select the keyframes and any other property I-beams you want and create the animation preset.
Now create your other drops, apply the preset and then offset them using their Anchor Points rather than their positions. This won't work if you're animating their scale or rotation however, because scale and rotation work around the anchor point.
Of course there's always different ways to do thing in AE. You can create particle systems using expressions, as Prof. Sparkles said. Here's an expression that you can apply to the position property of each bubble. Use two nulls to control the start, lifespan and wiggly-ness of the bubbles. It's not quite up to the trapcode preset, but whadayawantforfree?:
wigglespeed=1; //controls the frequency of the wiggles; change this to whatever you want
seedRandom(index, timeless = true); //create static random numbers
start=random(thisComp.layer("start").inPoint, thisComp.layer("start").outPoint);
//when the bubble starts, set by the in and out points of the start null
//only do all the hooh-hah if it's time to start bubbling (saves processor cycles)
if (time>start)
{
lifespan=random(thisComp.layer("stop").inPoint, thisComp.layer("stop").outPoint);
//how long the bubble takes to go up, set by the stop null's in and out point
posX=random(thisComp.width);
wiggleX=thisComp.layer("stop").effect("Point Control")("Point")[0];
wiggleY=thisComp.layer("stop").effect("Point Control")("Point")[1];
startY=thisComp.layer("start").transform.position[1];
stopY=thisComp.layer("stop").transform.position[1];
wigglepoint=thisComp.layer("stop").transform.anchorPoint;
//this should be [0,0] so that the wiggle doesn't introduce unweanted offset
posY=startY+(startY -stopY)*(start-time)/lifespan;
pos=[posX, posY]+[wigglepoint.wiggle(wigglespeed, wiggleX)[0], wigglepoint.wiggle(wigglespeed,wiggleY)[1]]
} else {
//not time to go yet
thisComp.layer("start").transform.position
}
For this expression to work you need two nulls called start and stop, and a point control effect (effect>expression controls>point control) applied to the start null. project file here