I know my answer is a bit late so I hope you will see it. I have taught mosaic art for over 15 years and made many birdbaths with all types of substrates and tessrae. My adhesive of choice for outside work is liquid nails for small projects in clear or working directly into your grout. For outside projects you want a sanded grout and to be sure your spacing is not to large for the grout you are using.
Proper preparation of your substrate is very important as well.
I have birdbaths that have been in my yard for more than a dozen years that look just as good as when I made them. I also teach tufa and concrete art which make very nice birdbaths, it all depends on what you want in the finished piece. Have fun, mosaic art is great therapy ( you get to break things for art (~ and it can be a completely upcycled art form.