Model paper wrapped bottle

Hello!

I need tips on how I could model something like this. I have some ideas, by they do not seem optimal: rotating a slightly larger mesh than the bottle mesh around with suitable falloff. Shrinkwrap the mesh and also screw it vith a modifier.

This is my result with that method:

Not entirely an adequate result imo. So, any tips are welcome!

Have you tried making the wrap as cloth and pinning it at top and hooking it to the bottom of the bottle?