It is important to remember that the depletion layer consists of uncovered charges neighboring the two sides. So, the p-side has an excess of electrons in the depletion layer and the n-side has an excess of holes.
In forward bias, the majority charge carriers on both sides move towards the depletion layer and thus recombine with uncovered charges of opposite polarity. So, the width of the depletion layer decreases due to the process of recombination of charges.
In reverse bias, the majority charge carriers move in the opposite direction, away from the deletion region. So, they leave more uncovered charges in their wake (electrons leave holes and holes leave electrons behind). This sudden formation of uncovered charges adds to the depletion layer and thus its width increases.
Regards