Locate your wall studs; you could verify by drilling a small hole through the grout line. After drilling the tile, (don't put your drill on "hammer") screw through the shelf and tile and into the studs with a stainless steel panhead screw.

Trebruchet, there's only one stud, so I'm stuck with two of the three screws going into anchors. Thanks for the response!

It depends so here goes.
Assuming it's a # 8 OR #10 - as the bore-countersink bore on your shelf will fit that screw. No Biggie, as a panhead will work equally as well.

Anyhow, you're looking at either a 3/16 or 1/4 drill bit, depending on what size anchor. Your anchor WILL tell you what size bit you need. If it's ceramic, any diamond bit will do. If it's porcelin, I would use a Armeg PTC bit (google it). THAT size is based on what sized hole is called for the anchor. Use a good anchor like these and call it a day. I would not loose sleep on hitting a stud with good anchors.

http://www.toggler.com/products/alligator/overview.php

Thanks so much, chefwong! I just watched a video of that drill bit going through porcelain like butter! Wish me luck...