What can you do to make sure a small piece of a bone from your thumb grows back?

Bone healing. I'm not sure what your original injury was, but bone healing is best in an atmosphere with good blood supply and no infection.
Needs Immobilization. It depends on where the piece is, the amount of blood supply to help heal it, and how stable or immobile the piece is. At times, a small fracture fragment may not heal bone to bone but merely attach by scar tissue which may work as well. An example is the very tip of the thumb. When involving part of a joint, healing becomes more critical, requiring proper immobilization by cast or surgery.