Jan Westphal shared the idea on Cigar Box Nation, and I was so blown away by the simplicity of the construction, I had to share it with you.
John suggested I post this jig in "Special Tools" so here it is. Its just two pieces of wood joined by two hinges (?) and two brackets* to hold the Dremel. The cut off whell is a diamond coated 1.5" one. The bottle rests between two pieces of metal glued to the wood and the clamp at the right hand side holds everything on the table and functions as an end stop for the bottle, sort of.
I thought it helps to wrap cellotape around the bottle neck to prevent from too much chipping but it is still necessary to take lots of time and dont rush it - I need about 5 minutes for one cut - turning the bottle all the time and taking it very slowly with some nice laidback music in the background. If I press down too hard little pieces of glass are coming off which results in awful lot of grinding afterwards.
*can be found in hardware stores, used to fix water pipes onto walls