The only way to achieve that round edge that I know of is a "soft fire" in a kiln.

That's what I was afraid of. I don't have a kiln though so was hoping I could accomplish the same thing - or approximately so - with a torch.

So, it's either sanding/grinding and polishing or a kiln to get a nice rounded edge then? I have a flat lap that makes it easy to get a nice finish on a flat edge (like when cutting a bottle) but it still leaves a fairly sharp/uncomfortable edge between that flat surface and the sides of the bottle. I've found a I have a difficult time angling the glass to get a nice even rounded edge on the outside edge - and because of the curve, can't get into the inside edge to round it at all. So was really hoping a torch would be the answer.

Back to the drawing board I guess!

A glass worker's torch might be able to do that -- I don't know but it might be worth finding out.

I would think that a belt sander used for such a thing or a glass grinder with a beveling kit on it would do the job.

I'm not sure if you need to have a shiny/polished edge, or just a smooth one. If you don't need a polished edge, I would use a stained glass grinder. I have gotten many years of use out of my Inland "Wiz" series grinder.

I use my stained glass grinder to round the edges of glass, especially when I am doing mosaics. Grinding leaves a dulled glass appearance. Easy to fix... just apply a thin layer of clear fingernail polish to these dulled edges. The rounded edge becomes shiny, blending nicely with the flat surface of the glass piece.