I also shape my necks by the facet method; usually five facets. I rough cut the facets with an angle grinder with a 60 grit disk, then all the rest is done with the Shinto rasp, large files, and hard sanding blocks.
I only use routing to cut the flat sides of the neck, and sometimes to define the flat back surface to the right thickness. My Luthier buddies who mostly make guitar necks use radius bits to get the shape close, and then use Shinto rasps and sanders to refine it. But guitar necks are usually thicker, rounder, and more consistent down their length. Bass necks, at least most modern ones, have a more complicated shape. The radius varies from the fingerboard edge to the centerline, and it also varies down the length.
Unless you are driving the router by CNC, or using a complex pattern-following machine, you are going to be shaping a bass neck mostly by hand. Some power tools will help save some time, but I doubt that the router with a radius bit will help you much.