I got this cheap glass cutter but unfortunately the ergonomically shaped handle made it difficult to position the cutting wheel perpendicular to the bottle axis, so I removed the handle.
I used a variety of objects to clamp down the cutter at the desired height with a clamp.
Then I simply pressed the bottle down and against the cutter. This is a bit tricky and a more elaborate jig might be useful, but when you are careful enough it works totally fine. You just have to make sure to press the bottle down enough so the score on the bottle stays at the same height.
Only rotate the bottle one full rotation, not more.
Then I exposed the bottle alternating to hot and cold water. After three or four dips in the water, the bottle usually cracks into two pieces. Ideally in a nice straight crack all around on the score line.
The tricky part now is to smooth out the very sharp edge. I experimented with a small Dremel grinding stone mounted in a water bath. Not ideal. The glass chipped out quite a bit. Maybe a bigger stone would have worked better.
I ended up just using increasing grids of sanding paper. First I made the cut completely level by turning the glass upside down and moving it over the sanding paper. By tilting it sideways a bit I was able to smooth out the outer edge. For the inside I used small bits of sanding paper wrapped around my fingers or a block of Styrofoam.
Finally I polished the edge with a buffing wheel mounted in the drill press.
I´m quite pleased how the glasses turned out. A more elegant way of smoothing out the rim could be to fire polish it with a torch while the class rotates on a turntable. I want to try that soon. Anybody got a turntable to sacrifice?
Edit: fire polishing worked out great. Watch a short video of the process here.