Now I understand what you meant by 'curved cylinder'. I didn't pick up on that. Here's a brief, simplified demonstration:
Once you've established the form of the bottle, the first step is to create a helix concentric to the bottle.
You will use this helix as the path of a spiral 'swept surface' feature.
Then you create a 3d sketch and select the bottle surface and the spiral surface and use the 'intersection curve' tool to create the helical path that follows the bottle curvature.
Finally, use this 3d sketch as the path in the 'swept cut' feature that forms your helical grip.
I've attached the model used in this tutorial in case it can be of help. I'm sure your bottle and grip will be much more beautiful than mine, this was just a quick demonstration of the features you'll need.