First, this is not a good application for a projected texture. The reason you’re getting a mirror image repeat is the texture is projecting all the way through the object–the reversed part of the image is where it projects all the way through to the other side. So uncheck Projected.
Also, you can wrap a texture around a single-curved surface–like the surface of a cylinder–with no problem. But you can’t wrap it around a compound curved surface, such as where the bottle starts to taper at the shoulder.
Look at bottles in the supermarket (or the liquor store), and you’ll see that the flat paper labels only wrap around the bottles where they’re more or less a straight cylinder, not where the section of the bottle changes (tapers or curves). The only exceptions are the plastic shrink-wrap labels that conform to the bottle contour. You’re stuck with the equivalent of a paper label, which can curve in only one direction, so you have to make a label that fits around the straight parts of the bottle body and neck. Try to size the label so that it is exactly one bottle-circumference in width (or an even sub-multiple) and one bottle straight section (straight cylinder) tall.
Here’s an example of a soda can I did a while back:
By all means, post some followup questions if necessary.
-Gully