Select a large, wide bowl (preferably glass) with a 4-5-quart capacity so there is enough space to hold the whole mixture. Put a small amount of vanilla pudding on the bottom of the bowl and layer one-third of the Nilla wafers to cover the pudding. Overlap the wafers, if necessary. Follow the wafers with one-third of the bananas and one-third of the pudding. Repeat the layers (i.e., wafers, bananas, pudding) two more times and then cover tightly with plastic wrap.