I know it's common for use with sheet rock in a dremel. The last 1/4" of the bit is smooth so can be used as a guide on any hard surface. I imagine the same bit could be used in a router with an adapter for the shank size. Lowes sells them Roto Zip brand part number GP8.
If you want to pre-dill a hole in the center of the cutout so the bearing can go into the void and be used as a guide, there is also a guide bit for the router. The bit is commonly used for trimming formica counter tops. Again, available at Lowes. They call them trimming bits. Two part numbers I found at Lowes are 63621 and 28843.
