I've drilled flat glass, not a bottle, but I would drill with Dremel and water with ceramic/Aluminum Oxide/diamond bits. You have to go very slow toward as the bit just break through the back, or it will cut chipped and jagged. Better to start with a small diameter bit and work your way up.
Heat the bottle to 850-900F in a kiln.Then use use a hand torch to very lightly fire polish the jagged edges of drill hole while it is in the kiln, then anneal.
If you don't have the kiln or torch, wrap a small diameter dowel with silicon carbide paper, and under water, gently polish the hole. Maybe 320/400/600 grit.