I'm drilling holes into glass wine bottles, using a masonry bit, so far I've not had a problem. I have a variable speed drill, set the bottle on it's side in the kitchen sink, on a towel, I run the faucet on it at a trickle, start drilling slow, then speed up, in usually 2 - 3 min, I'm through.
My problem is, there are small spider cracks. How do we prevent that?
I've drilled about 20 bottles, could the bit be dull already?
Are there special bits for glass drilling?

Too much pressure is causing the cracks. You should be using a ceramic bit rather than masonry or something like this Glass Drill Bits

Please show a picture of the drill bit you are using. A masonry bit will not drill glass.