I've just begun drilling holes in wine bottles so I can put lights in them. First, you need a glass/tile bit, not just any old bit. There is very little dust when you drill. It doesn't hurt to have a spray bottle and spritz a little water on the hole as you are working on it. The biggest concern is if you do something dumb and break the glass. For example, a hole I drilled wasn't large enough, so I tried to drill another hole next to it to make one bigger hole. Not. When the bit went through, the bottle shattered. I drill in my kitchen, on a pad of newspapers. I put them on a chair, since it takes quite awhile to get a hole thru glass and holding the drill above a normal position for my arm is difficult for any length of time. The masking tape is a good idea, prevents any chips as you are drilling. Good luck and have fun.

Glass dust? I've never had any problem with it. You do generate a small amount of dust but since you should be using a cutting fluid of some kind almost all of the dust winds up as a small amount of glass "sludge". A cutting fluid is very important as the drill gets quite hot due to friction. The heat can dull your bit so keep the bit lubricated while drilling. I use 3-in-1 oil, a friend uses veggie oil and some people use water.
I've drilled glass in the garage, the house and outside and have never had a big mess to clean up.
If the hole you drill is too small, drill out the hole using a larger bit. You can't enlarge a hole, in glass, by drilling another hole next to it. Well, at least most of time you can't. Remember glass is a crystal and not a fiber like wood. Crystal will fracture, crack and shatter, fiber can be sheared or torn.
I've never used masking tape but I haven't needed to. I'm sure sometime in the future I will take advantage of it. If your drill bit is skittering around by all means use a bit of tape to stabilize it.
Always wear eye protection of some kind. Set up your glass drilling operation in an area that is easy to clean in case the glass shatters. Also set up your drilling area at a comfortable height, you will be holding the drill for awhile. If you're worried about the glass shattering and your getting cut, wear gloves.
While drilling, NEVER force the bit! Let it chew it's way through the glass on it's own. Forcing the bit can lead to the glass shattering. Also, tempered glass doesn't drill very well if at all, don't waste your time on it.
Drilling glass isn't hard, just a little time consuming. Plan on taking your time and you will have success!
Good luck!