BiTeI has a layered and noncentrosymmetric structure where strong spin-orbit interaction leads to a giant Rashba spin splitting in the bulk bands. We present direct measurements of the bulk band structure obtained with soft x-ray angle-resolved photoemission (ARPES), revealing the three-dimensional Fermi surface. The observed spindle torus shape bears the potential for a topological transition in the bulk by hole doping. Moreover, the bulk electronic structure is clearly disentangled from the two-dimensional surface electronic structure by means of high-resolution and spin-resolved ARPES measurements in the ultraviolet regime. All findings are supported by ab initio calculations.