In order to Focus on your question I will Keep the bottle thread out of the tutorial.
Answered with a tutorial: https://grabcad.com/tutorials/how-do-i-add-a-specific-cut-pattern-with-a-draft-around-a-curved-surface
The above one is long process...
USE "WRAP" FEATURE..
IT'S very easy select "WRAP" from features and sketch on the body and selcet whatever you want... "EMBOSS" "DEBOSS" "SCRIBE"
Wrap Feature does not work on non cylindrical face.. Thats why the steps mentioned above are Long..