The key is in the joint between water bottle and the pressure source (I just use the garden hose). It needs to allow enough pressure to build up within the bottle, and unhook when you release the bottle. I hooked up something like this to my garden hose and put several layers of masking tape on the top left part to snugly the water bottle over it.
Fill the water bottle with 1/3 water (so 2/3 air), and hook it up over the masking tape. Hold it vertically (upside down) and turn the water on, pressing down to hold it in place. Do NOT hold your face or any other body part over the bottle. The incoming water will compress the air inside to about half its normal volume. When there's about 2/3 water inside the bottle you won't be able to hold it any more, so let the bottle take off vertically. It should go about 25 or more feet in the air.