If the amplitude of primordial gravitational waves is measured in the near-future, what could it tell us about bigravity? To address this question, we study massive bigravity theories by focusing on a region in parameter space which is safe from known instabilities. Similarly to investigations on late time constraints, we implicitly assume there is a successful implementation of the Vainshtein mechanism which guarantees that standard cosmological evolution is largely unaffected. We find that viable bigravity models are subject to far less stringent constraints than massive gravity, where there is only one set of (massive) tensor modes. In principle sensitive to the effective graviton mass at the time of recombination, we find that in our setup the primordial tensor spectrum is more responsive to the dynamics of the massless tensor sector rather than its massive counterpart. We further show there are intriguing windows in the parameter space of the theory which could potentially induce distinctive signatures in the B-modes spectrum.