Alla - If you do the drilling with the glass and bit under water, you greatly reduce the likelihood of breakage. When I was in school (I'm a ceramic engineer by education), we used to demonstrate by cutting microscope slide slip glass (really thin) with scissors. It seems that the water molecules race in to the microscopic fracture and bind with the exposed bonding sites, reducing the stress.

I use a plastic tub full of water that's about 1/4" deeper than the height of the glass vessel. That way it becomes a 1-man job on the drill press.