You might also try filling the bottle with hot/boiling water. This should help soften the glue and make it easier for it to stick to paper towels... I noticed something similar when I drain the grease from hamburger meat into a used can (vegetable, soup, etc). After a moment I have to be careful where I put my fingers on the can because the glue stops being tacky and becomes more liquidy, which will smear all over my fingers... If you think about it, it makes sense, considering the glue is probably applied from a hot glue gun originally...
For that little bit of glue residue (like from price tags and the like), I've found that Puffs Plus work great. They get into the glue and cling, meanwhile the little bit of lotion gives a bit of lubrication to keep from scratching the surface. This may or may no help because you do have to press firmly, and the thin walled water bottles may just crumble. It might work best if once you remove as much as you can with hot water, fill it with cold and screw the cap back on. The water should he resist the pressure of rubbing.
Caz