This is on the assumption that you have not accidentally poured water on the outer surface of the bottle (no matter how little) - i.e., this surface is perfectly dry:
Note that air (the atmosphere around us) contains water molecules as well.
When you put cold water into a plastic bottle, due to condensation$^1$, water will collect on the outside of the bottle$^2$. Since water contains ions (and is therefore conductive), a capacitive touchscreen will react to such a surface in contact with it.
Water collects as droplets on a cooler surface when warmer air is in contact with it. In this instance, the outer surface of the filled bottle becomes cooler then the surroundings (which is assumed to be warmer i.e., you're not in a cool environment, but for example, you are inside your home).
I know that maybe not much water will collect when using standard tap water (because it is not that cold), but because the water is pretty much cooler than room temperature, some condensation will occur and my understanding is that some of these capacitive screens are pretty sensitive.
Capacitive touch screens react when any conducting surface (like your skin) comes in contact with it.
It is well known that a bottle filled with salt water can behave like a capacitor since salt water is an electrical conductor.
It is also known that tap water does contain charged particles, so it may be the case that a bottle of water can also behave (albeit much less pronounced than with salt water) as a capacitor.
How to test if both the above explanations are valid:
Redo your experiment, this time:
Use warmer water to test the validity of the the first explanation.
Try using distilled (pure) water to test the validity of the second explanation (distilled water has no conductive properties). If available, dip the two ends of a multimeter in the distilled water to indeed confirm it contains no anions/cations.