Place the oil drip pan in a warm, sunny location receiving eight to 12 hours of bright light daily. Fill the pan with an even layer of pebbles or pea gravel.
Nest one bucket inside the other. Measure the height difference between the tops of the two buckets. Remove the inner bucket. Add ½ inch to the measurement and mark it from the ground up on the side of the outer bucket, using a black permanent marker.
Drill a 1/16-inch hole through the side of the outer bucket at the black mark. Place the bucket on top of the pebbles in the center of the drip pan.
Turn the inner bucket upside down and drill 10 to 15 1/16-inch-diameter holes in the bottom. Measure the width of the plastic tubing. Mark and drill an additional hole to one side and through the bottom of the bucket for the tubing.
Attach the airstone to the plastic tubing. Place it in the outer bucket, or reservoir. Feed the tubing up through the hole in the inner bucket, and then insert the inner bucket into the reservoir. Pull the tubing up the side and out of the bucket. Attach to the aquarium pump.
Mix equal parts vermiculite, perlite and peat moss. Moisten and mix again. Fill the inner bucket within two inches of the top with the planting mixture.
Scoop a small hole in the center of the bucket and Insert the banana rhizome, covering it with 1/2 inch of planting medium. Cover the planting medium with 2 inches of mulch except for a 6-inch circle over the rhizome.
Mix the hydroponic fertilizer with water according to the manufacturer's instructions. Pour the mixture slowly into the bucket until it comes out of the in the side of the reservoir.
Plug in the aquarium pump and turn it on.
Monitor the rapidly growing banana, adding water as needed to keep the reservoir full. Add water to the drip pan as well to raise the humidity in the air. Mist the banana daily with a spray bottle.
Add hydroponic fertilizer weekly.