The best way to grind/shape the top surface of your cut glass bottles is with a disk grinder, such as the Glastar (G9) Disk Grinder. This grinder has a 6" diameter disk, so you can grind/shape a 2-3/4" bottle in one pass. The result will be a perfectly square, flat edge.
There are other options, you can grind/shape the cut edge with the Gryphon Wet Belt Sander that has a 3" wide belt, or with a standard router-type grinder by using a straight-edge guide to help keep the glass edge straight against the grinder head. A straight edge guide is included with the Glastar All-Star (G8) Grinder and we currently have a few Special Edition versions of the Diamond Star (G14) Grinder that also includes one as a FREE accessory. We also sell them individually for $12.55.
The best way to polish the sharp edges on the inside and outside lips of the cut glass bottle is with a kiln. On a "fire polish" setting the kiln will melt the sharp edges perfectly to round them over and polish them. This will, of course, ruin any labels or art work that you may be trying to preserve on the bottles.
For a cold method of smoothing/polishing the tops and outside edges of the bottles, finer grit disks and polishing pads on the disk grinder or belt sander will do a good job. The cork belt on the belt sander gives a final polish. These methods will only smooth/polish the top and outside edges. For the inside edge you will have to rub them by hand with fine grit emery cloth or hold the cut bottle over the router head on a router-type grinder to get to the inside edge. We have finer grit grinder heads for the router-type grinders that will smooth the glass surfaces but it will still look "milky"; smooth to touch but not truly polished.
Note: All prices in US Dollars