I think you're right about the drill, made an attempt with a cheap guitar neck I found and the bit does find it's way out of the neck! An auger bit might be better as it has less chance of wandering and removes excess material well, so less burning. It could be done but the problem remains the same how to do it on a bass neck; I may have the answer but I need to give it a go to see if it works and is an easily reproducible technique. Stay tuned
Scott