@Sara-S , I made it in the same way I’d make a simple draw string bag.
I measured the circumference of the bottle, added about 1-2 in for seams and ease of putting on and then made a quilted bit of fabric, with 2 pieces of cotton fabric and an off-cut of cotton batting, trimming it to the right length and width. I made sure I made it extra long to begin with, as I knew I’d have to make a turned over channel for the cord at the top.
I then sewed the side and bottom and squared off the corners by sewing a seam 90 degrees to the sides and cut the little triangles off before finishing on the inside with zigzag.
You could add a proper casing so that you could run 2 cords through to make proper pull cords, but I just cut it to the right length and turned over the top, threading one length of cord through it.
Hope that makes sense. DH promptly lost the bottle on the golf course ( the second this year!) , so I may have to make another.