Classic
The only necessary outer design requirements for the bottle rocket to fly are the nozzle for propulsion and the flaps on the parameter of the bottle to stabilize it during flight. Use thick construction paper or cardboard to cut out four triangles with the angles being 30, 60, and 90 degrees. Now you have made yourself quick rocket stabilizing flaps. The flaps will prevent your bottle rocket from pitching and rolling in the air.
Nose Cone
The drag that is causes by the bottom of the bottle will make it harder for the rocket to achieve its maximum height. By constructing a nose cone to deflect the airflow, you will greatly increase the flying height of the bottle rocket. Again, using construction paper, form a cone shape. The larger end of the cone should be the same diameter as the bottom of your bottle. Attach the cone to the bottom of the bottle with either craft glue or tape.
Double Decker
To elongate your rocket and to raise the center of gravity a bit you can add the lower portion of another bottle the same size of your rocket bottle. Measure to about the half way mark in the second bottle, and cut it in half. Apply glue to the inside rim and place it on top of your rocket base. If you created a nose cone, you can put it on the newly constructed rocket tip.
Hidden Parachute
Building off of the previous construction method, you can add a parachute compartment in the top of the rocket. Using that same half piece of the second bottle, also cut off the bottom of the bottle then glue it to the top of the rocket body. You can fold and attach a neatly folded parachute made out of a garbage bag, inside the cavity at the top of the rocket.