Macroscopic ferroelectric order in alpha-GeTe with its noncentrosymmetric lattice structure leads to a giant Rashba spin splitting in the bulk bands due to strong spin-orbit interaction. Direct measurements of the bulk band structure using soft x-ray angle-resolved photoemission (ARPES) reveals the three-dimensional electronic structure with spindle torus shape. By combining high-resolution and spin-resolved ARPES as well as photoemission calculations, the bulk electronic structure is disentangled from the two-dimensional surface electronic structure by means of surface capping, which quenches the complex surface electronic structure. This unravels the bulk Rashba-split states in the ferroelectric Rashba a-GeTe(111) semiconductor exhibiting a giant spin splitting with Rashba parameter alpha(R) around 4.2 eV angstrom, the highest of so-far known materials.