Here's a post about using satelite dishes for some other projects- maybe it'll give you some ideas! http://www.hometalk.com/470708/using-old-satellite-dishes-for-planting. Your idea for the bird bath sounds very cool.
I've been wanting to make a mosaic birdbath out of something repurposed as well. Instead of a satellite dish I thought I'd like to use an old disc from a plow. Some of them even have pretty scalloped edges. If I can get one, I'll tell you how ti works out.
We have a last chance Goodwill store where dishes are .15 each..You could smash them up and use the pieces. Home Depot will be able to tell you what sort of grout to use that will be weather resistant. What a fun project!
I love the look of mosaic, and have done it a few times. I use crash glass on all of them, because I love the look. Just get those tempered glass panels, you can get them online fairly cheap, set it on a sheet or pillowcase and pull up the edges to contain the glass, tip the panel on end, so a corner is pointed up, and hit it with a hammer, then empty the pieces in a box. You end up with a sheet full of broken glass, but in chunks with cracks running though it, so try to keep them in bigger chunks. Sponge on some color to your dish, and sprinkle glitter on top (if you want), then wipe each piece of glass with alcohol to clean it, put a glue that dries clear on each piece and attach, let dry. Mix "unsanded" grout, it comes in several colors, I like black. It won't scratch like the sanded grout. Wipe it on glass with fingers (wear gloves) or there's a tool you can buy, then sponge off with a damp (not wet) sponge. Wait until it's dry, and voila! Gorgeous birdbath. Not sure what the birds will think about the glitter, so you might skip that step, it'll look good either way, I just like glitz. I use the big glitter, but if you sprinkle the finer glitter on each color, the same color, it won't be so bad, and just up the wow factor slightly, that's up to you. When you get the grout, it should say how it will withstand being outside, you might have to seal it, all my projects are indoor (trays, bench, etc). Good luck, I'm sure it'll look great no matter what you do with it. Very unique.
Draw or trace the design you want onto the dish with chalk or a magic marker. Then fill in the outlines with the different colors you need. I would use thinset (a concrete-like substance you mix with water) to adhere it since it will be outside, rather than using glue. Let dry overnight or longer and then mix grout and apply with a rubber trowel.