I'm just going to describe another way of scribing the score line for cutting your bottle. Please see the rest of Fstedie's excellent guide for instructions on how to candle the break and smooth the cut.
Step 1: The Jig Is Up
Lay your wine bottle in the gap and adjust the glass cutter so it rests on the wine bottle. You will be rotating the bottle while pulling the bottle toward the cutter, so it needs to be snug, but as long as you have contact the fit doesn't seem to be all that critical. See the intro for a pic.
I found this nice pro style glass cutter in the gutter - the dinky little .99 cent ones may not want to clamp on as easily, so you may need to make a little cradle for yours to keep it from moving in the clamp.
Note that I got in a hurry taking pics - you'll need to remove the labels from your bottles first. You can cut above the labels for tall glasses and leave the labels intact if you like, but you'll have to be careful with the burning candle part to avoid damaging them.
If you do try some cuts with the label on, you'll probably hit "bumps" as you rotate the bottle since the sharp edge of the Workmate top will want to tear into the paper. Some masking tape wrapped around the bottle in a few places would probably fix this issue.
Step 2: Cradle to Grave
Position another clamp at the back of the bottle. I use a bigger 3' long nylon clamp for this step since it sticks up a bit higher than my one footers and makes a nice backstop for the wine bottle. Or clamp a 2x2 stick of wood back there.
Step 3: Take the Position
My cutter has a built in oil supply, but you may want to lube the bottle a little to help score the cut.
Now you are ready to cut. With your gloves on and your safety glasses in place, you will rotate the bottle toward you with a bit of a pull toward you, making good contact between the bottle and the cutter. It shouldn't take a lot of pressure to make a nice scored line.
Unless your clamp shifts, your scored line should meet itself as you complete your rotation.
Step 4: Drink Up
Ok, here's the jig with a scored bottle in the background, ice water for cooling the crack and note how the candle rests in one of the Workmate holes.
But I found it easier to put the bottle back in the gap and hold the candle underneath while rotating the bottle.
I was too stingy with the water at first. Put a bucket down there and dribble plenty of water on the hot scored crack. I used almost a whole glass on my second attempt and the top dropped off into my bucket as pretty as Anne Boleyn's head.
Score cracking details are better explained in Fstedie's Instructable .