The breaking of bulk inversion symmetry in ferroelectric semiconductors causes a Rashba-type spin splitting of electronic bulk bands. This is shown by a comprehensive mapping of the spin polarization of the electronic bands in ferroelectric α-GeTe (111) films using a time-of-flight momentum microscope equipped with an imaging spin filter that enables a simultaneous measurement of more than 10 000 data points. The experiment reveals an opposite spin helicity of the inner and outer Rashba bands with a different spin polarization in agreement with theoretical predictions, confirming a complex spin texture of bulk Rashba states. The outer band has about twice larger spin polarization than the inner one, giving evidence of a spin-orbit effect being related to the orbital composition of the band states. The switchable inner electric field of GeTe implies new functionalities for spintronic devices.