Sliced bananas tend to turn brown quickly due to exposure to air and the release of enzymes that cause oxidation. Using just barely ripe bananas will help. Also, try to keep the bananas covered with pudding to prevent air exposure. If you want to serve with bananas on top, wait until just before serving to add those. You can dip the sliced bananas in any acidic fruit juice, like lemon juice or lime juice. This does change the taste a bit, using club soda can also be used and will not change the flavor.