I want to inset a mirror into the underside of a jewelry box lid. The lid is 3/4" walnut. The mirror is about 4x6x1/8" thick. One thought is to use my router with a bushing and straight bit. And use a template slightly larger than the mirror. I have a 1/2" straight bit, but it won't plunge into the wood because there is no carbide on the bottom of the bit. This seem like a common operation. Is there a better way?

The bushings came with the router (Bosch) and I've never used them, so any tips are appreciated.

Also, what kind a glue would you suggest to attach the mirror?

Mitch