Step 5: Wire it up (this is familiar...)
Strip two pieces of solid wire long enough to stretch from the holes to where you intend to mount your piezo- allowing plenty of extra length leaves you space for multiple strain reliefs (pieces of electrical tape). Strip at least 1cm from one end of each, and bend these ends at a sharp right angle. Insert the longer stripped ends into the electrode holes. Arrange the wires so that the tips are 5mm apart or closer, and firmly tape (and preferably hot glue) the ends in place.
Attach the other ends to the piezo. Solder is not necessary at this point, one of the principal joys of working with piezo sparkers is that the spark can jump millimetre gaps in wiring so contact joints are perfectly good enough. This is also one of the principal frustrations of working with piezo sparkers- several types of tape are considered a conductor by the spark, including possibly duct tape. When possible use electrical tape, heat shrink or solid plastic to insulate the wires.
Firmly attach the piezo to the outside of the bottle. If you are using only the element, you may want to consider how to insulate the two wires from eachother to prevent it sparking over.
Realise the flaw in your plan- plastic bottles tend to deform under lateral pressure such as is required to operate the sparker button. Improvise and attach some long rigid object underneath the sparker to distribute the load- what else but the ubiquitous bamboo skewers? Realise this isn't much better, but in the absence of PVC pipe it will have to do.