Woodcut handle
Your Woodcut Bowlsaver handle has a 1/2 inch bore. Thus any tool with a 1/2 inch shank should work. Woodcut offers an unguarded cup cutter with a 1/2 inch shank that works well in this handle. Being unguarded, particularly for someone with little experience hollowing, it is better suited for goblets and other open forms where you can keep an eye on the cutter while gaining experience determining the best orientation of the tool. You can also fit 12mm tang tools like the Vermec hollowers. The fit is just a little loose, but easily acommodated by the set screw.
Your handle is a little short for deeper hollowing, but one thing that I have found improves its function is to make up a wooden or plastic plug for the tool end, then fill the back of the handle with lead bird shot (available from most gun shops). The added weight and damping will likely be most appreciated, and should you not like it, is easily removed.