Here is what you need to do it correctly:
www.CRlaurence.com has Diamond Tool Coolant Cat. No. DTC8oz
You can also buy a rubber suction ring to keep the liquid pooled.
This is a concentrate. 1 part coolant to 50 parts water.
This is a severely Hydrotreated Petroleum Oil that is water soluble. Using water will work but still takes some life out of the bit long term. It also doesn't cool as effectively as the coolant mix and breaks, cracks, and chips do occur more often when using just water or veg. oil.
It shouldn't take long to drill, I drilled 3/8" holes yesteday and it only took maybe 10 minutes total for 2 holes with the proper bit and coolant.
I used a roll of paper towels and a small bucket with a paper towel on it pressed against the other side of the glass to catch the cutout and liquid after the hole is drilled.
Don't be afraid... It's Only glass. Just need to slow the drill down right before it punches through or it will chip severely.
I have drilled hundreds of holes in glass successfully. I have over a 99% success rate in this department.