Spindle diameter is another thing to consider. A big diameter will grab the string better, but according to what I've read and experienced you don't want the spindle to be too thick down at the hearthboard end... half an inch might be a good size to experiment with. But I am sure other folks will have other ideas.
What you might want to try and something that I usually do is I leave the part of the drill larger in diameter where the string rides and smaller where the drill meets the hearth. Some people will tell you that this slows down the working end, and of course, they are correct, but I haven't found it to be a problem, in fact, the reverse is true due to increased traction (right word?) between the drill and the bow string.
You might like to try the Egyptian method of fastening your bow cord to the spindle. This involves a simple knot and more wraps of cord around the drill than the set-up you generally see where the cord just goes once around the spindle. I generally use just the single pass method nowadays, but I have used the Egyptian method a lot... especially when I first started and the drill kept on flying off into the air.
Coote, as always, has an excellent suggestion - the Egyptian bow drill should solve your problems re: string slippage, but I still prefer the other method. Maybe because I worked long and hard to learn it. If you use the Egyptian method, you can use a constrictor knot around the drill. I find this works well.
Here is a web page where you can see the Egyptian method (Primitive Ways):
http://www.primitiveways.com/#anchor694080
If you aren't making much dust, then maybe you need push harder down on the spindle.
Coote, I think his problem here is his choice of materials, as mewolf1 already mentioned, although in a lot of cases, you would be correct.
If you are keen and persistent, you should win.
No argument here - I learned how to do the bow drill method of friction fire by practice and what I could find to read. I won't tell how long it took me (don't want to discourage you) but there is more than enough people willing to help you, that it shouldn't take you any time at all.