Clint, that's usually done with heat in a kiln.
Glass melts and I'd have to look up the temp, but you can attach a wire around the lip or rim of the top of a bottle and suspend it inside the kiln. If the kiln has an auto shut off, just set it for the melting temp, and not a single degree hotter. The glass will soften and the weight of the bottom stretches the neck like that as it starts drooping.
But the heat has to be totally controlled otherwise the entire bottle will be a molten melted mess.
The top lip usually has to be cut off then because the wire might embed itself in it, but that's easy to do with molten wire or with glass cutters.
You can also turn bottles sideways and let them collapse as they melt from the heat. I'll see if I can find some examples on the net. Anyway, that's how it's done. We used to do it sometimes in some of the art classes I taught, a break from throwing pots on the wheel. If you melt them just right they make great little serving trays and the neck becomes a flat handle for the tray.
I'll be back if I can find some images or a link.
