I don't think this is something that would be resolved (or caused) by a GFI device. I believe that you have two different ground potentials, and the wet bather is feeling the difference in potential between them. The two key elements that stand out are the plastic water pipes and the hydro massage tub (which would be/should be properly grounded).
This is a stretch and I admit I am only speculating, but the first thing I would try was to bond the metal plumbing fixtures of the shower (head, valve, and drain cover). I would also confirm that the tub is properly bonded.
Any metallic components in the water system near the shower could experience capacitive coupling with nearby circuits, and their voltage would rise significantly due to their isolation. I am sure the tingling would be short-lived, but nevertheless noticeable to a wet bather. (hmmm, maybe you could ask for an in-use demonstra.....nah, never mind:grin:.)
Oh, you might be able to detect the possible differences in potential with a high impedance digital volt meter, and this would narrow down what components are well grounded versus those that are not. Make sure that any fans or lights that are normally operating during her bathing are also operating during your inspection.
The confusing part is that the bottle is sitting on fiberglass. It may not actually be the bottle that is making her feel the tingle, but the change in body position, such as stepping on the drain cover in the process. I joked about the demonstration, but that might not be a bad idea (dry environment of course) if you can't isolate any other source.