[Speedslug]

The way I look at it heat control is going to be a very important issue with any torch work.

Glass doesn't like to have inconsistent temperature in things as thick as bottles nor as large as something that you would drink out of.

If you are already cutting the "tumbler" out of the bottom part of the bottle using a wet saw I suggest you just continue to use the abrasive cutting wheel as a wet sanding surface and soften the edges of it by tilting the piece to round over the edge.

Don't get me wrong, I know that it can be done a torch but I think the skill learning curve can use up a lot of bottles due to heat control problems as well as annealing the whole tumbler once you have the cut edge shaped.
And you will want a kiln for annealing. They are not outrageously expensive but they do run a sizable chunk of change.
That learning curve can use up a lot of patience as well not to mention that breakage will leave you with scalpel sharp pieces of unpredictable shapes.