I suggest trying to get some mirror adhesive (caulking) from a local glass shop. After the tile and mirror installation, sealing the edge of the mirror with silicone is the key. Most new mirror installations sit directly on countertop backsplashes (maybe on a couple of glass shims), and are caulked vs. the old method of sitting in a J channel. Moisture would accumulate in the channel and start delaminating the plating of the mirror.
It is also very important to make sure your bathroom has good ventilation. If you visit my website, I have a photo of a tiled mirror application in the gallery under the Ceramic Tab, Rollover #1 found here.