Is there any way to melt a perfect circle in a glass bottle?
No, with the possible exception of very thin laboratory borosilicate (Pyrex) glass. An ordinary glass bottle will shatter if you apply a torch to it unless it has been preheated to about 1000F and then you are working with a torch next to a 1000F bottle and its kiln. You do not have to buy a diamond core bit, but the alternative is a brass core bit (which costs a bunch less) and abrasive grit, a drill press, water, and patience. Glass has to be ground or drilled with water because if it gets locally hot, the stress will crack the glass. If you want a hole less than half an inch there are other drill choices. http://users.ticnet.com/mikefirth/coldwo… If you want a larger hole, it is possible to work with Dremel tools (although Foredom type with the extended shaft are safer around water) and stained glass wet grinders would allow you to increase the size of a hole.