VideoHacker

Use time or frames to start i.e.:

frameToStart = 39;
if (timeToFrames() > frameToStart)
{ wiggle(2, 500);
} else {
value;
}

That starts at frame 39.

or

timeToStart = 1;
if (time > timeToStart)
{ wiggle(2, 500);
} else {
value;
}

that after 1st second.

Reference:

How To Start And Stop Wiggle In After Effects At Specific Time

1. create a null layer
2. then use motion tracker track 1 point
3. apply X and Y to null layer
4. Create new BULGE effect in a new Adjustment Layer
5. alt+click the Bulge Center timer icon
6. in the expression area, select the pickwhip icon, and select the Null’s position, that’s it!

Reference:

Help getting distort->bulge to follow motion tracking? from AfterEffects