Summarize:

Purchase a small tube of sealant meant for fixing aquariums, or other leaks. Pipe a thin band around the joint between the gasket and the bottle. If you need to, use a popsicle stick or a toothpick to smooth the sealant down. Allow the sealant to cure. You may need to seal the area between the gasket and the tubing itself. You don't really have to do this, but it will make filling the bottle easier. You can also cut it off only partway so that it's still attached to the rest of the bottle by a "hinge." This will allow you to partially close the opening.
Seal the area around the gasket and tubing. Cut the top part off of the bottle, if desired.