Sorry for the confusion Robert,

If I can simplifies the procedure (and I welcome any 2nd opinions):

Your pics 1 and 2 shows how the first step is to make the openings in the outer surface.
In the Pics 3 and 4, the yellow surface simply represents a temporary extrusion made from the shape representing the inside perimeter of the handle.
The extrusion starts at exactly the middle point of inside of the bottle. Pics 4 and 5 shows a Blend (in the Construct menu) which has been made between the outside opening of the bottle and the edge of the temporary extrusion surface.
After the Blend surface is created the extrusion surface can be deleted. A second Blend can now be made between the edge of the first blend (in the middle) and the opposite outside opening of the bottle.
The purpose of the extrusion from the middle was to ensure that the inside surface of the handle occupies and exact position.

This was but one way to go about creating such an organically-shaped opening.