Step 1: Jig? Yes Please!
Step 2: Cut the Long Cuts
Remember that the glass must be fully supported under the glass-cutter. This is where you would get in trouble with any remnant of the bottle's shoulder, as it will create a gap, a ruined bit of glass, and a debilitating wound.
Perhaps a firm-but-slightly-yielding material would fix this? Or a setup akin to an English Wheel?
Score the glass, than tap along the line. The first cut won't visually separate but you will hear when it gives up the ghost. Mark your next line, score, tap, the tile will fall off, et cetera.
Step 3: Finish
Wash the tiles of the cutting oil with soap and water. For consistency and to hide the thinset I painted the backs of the tiles with spray paint. Experiment with colors and densities. I used pretty cheap spray paint so I probably used more coatings than you might need.
So go procure some bottles and please post pictures of what you make!