If that grapefruit juice does speed metabolism and burn fat, when is the most effective time to drink it?

Depends: The pro-metabolic effect of grapefruit is hard to measure precisely. Based on what we know about energy metabolism after periods of exercise, most carbs go back into muscle to replenish glycogen stores and therefore are not transformed into fatty acids and therefore not stored as fat. So, it makes most since to consume it in between meals or with a snack to keep the metabolic engine humming along.