The best, and certainly safest (but you still have to be very careful!) way
to cut a bottle is with a ... bottle cutter!
The UK based Craft Ideas web site informs us that a bottle cutter doesn't
actually cut bottles, but rather helps with the process.
"Perhaps rather surprisingly, bottle cutters are not actually used to cut
bottles, but rather to score a line over the surface of a bottle, which can
then be gently heated and cooled until it breaks along the score line."
Over the years, several companies have made bottle cutters, including the
well known late night infomercial Ronco. These days, there are two main
brands sold, Armour and Ephrem's. Each have their strengths and weaknesses,
so you should check them both out.
Tracy's Stained Glass Workshop has a representative page on Armour's.
"Armour Bottle & Jar Cutter
Alpine Stained Glass & Door covers Ephrem's version.
"Ephrem's Bottle Cutter
If you enjoy eBay, you can check out the various auctions and "Buy It Nows"
of bottle cutters, including "mint in box" (MIB) Ronco and K-Tel versions,
as well as Armour and Ephrem's bottle cutters.
This eBay auction/"Buy It Now" listing features an "old school" version.
"This is my newest styled bottle cutter. It is made of very sturdy aircraft
aluminum ... [Buy It Now] $34.95"
If you need any clarification, please feel free to ask.
Personal experience with cutting glass.
Checked eBay as noted above.
Google search on: bottle cutter
Google's Froogle search on: bottle cutter
Looking Forward, denco-ga - Google Answers Researcher