all well said Suzanne. The only thing I would like to add about the tumbling that seems to be misunderstood is the various compounds that clean to different degrees. A simple cleaning with aluminum oxide that I buy from the jar Doctor does not remove glass, it is simply removing stain on top of the glass, it is a cleaning compound. The different degrees of cutters can lightly grind that will not remove embossing to cutters that can remove embossing within hours. Suzanne described the reason for the dullness very well. To remove it with tumbling, you would first have to use a light cutter to polish the dremel marks left behind, and then follow with an aluminum oxide to restore the sheen. You could probably polish a small area like that by hand also with super fine sand paper, but that is not my area of expertise.
Filling the bottle with water first should help wth heat..ORIGINAL: Wilkie
I tried using a dremmel on a bottle once, there was a slight crack that I couldn't see and the dremmel caused it to spread. The friction caused heat, so keep that in mind when doing that.