Well, this is a pickin' technique that really goes along with proper muting. It depends on the effect you want so lets try a couple of things.

If you want just the string(s) you are picking to ring out by itself, then it is important to mute the string after you pick it and before you pick the next one(s).

If you want the string(s) to continue to ring a bit while you pick the next one(s), then you must mute those strings with the your pick, after they ring for the amount of time you desire.

As you move the bar downward as your picking down the strings; mute the ones above with pick; before you play the next one(s) down.

If you want the string to ring after the bar moves down from it; then mute the string(s) with either the pick, or extra finger that is extended.