I use regular jobber style bits when I drill them. Sometimes I use water, other times not when drilling. Just depends on the mood I am in and how much of a mess I want to make. If the blank is drilling hard, then I'll add some water to keep things cool. Redwood burls are softer, and they'd be a candidate for not using any lube. But more dense stabilized burls may need some water to keep things cool during drilling.
As for finishing, the sky is the limit. The burls have lots of checks and voids, so I typically have been sealing them with CA glue before I apply my final finish.
Brian