Come to Mama! Really there's a bath and body shop called Mama (in Avondale Estates and Krog Street Market). It's a local business with handmade goodies including soaps, lip balms, scrubs, essential oils. They also teach classes if you want to learn how to make your own soaps.
Another zero waste personal care option is LUSH (Lenox Mall); they have a wide variety of unpackaged products including soap, scrubs, fizz balls and deodorant bars.
You can get unpackaged soap at Sevananda and Whole Foods also.