We study asymptotically flat black holes with massive graviton hair within the ghost-free bigravity theory. There have been contradictory statements in the literature about their existence—such solutions were reported some time ago, but later a different group claimed the Schwarzschild solution to be the only asymptotically flat black hole in the theory. As a result, the controversy emerged. We have analyzed the issue ourselves and have been able to construct such solutions within a carefully designed numerical scheme. We find that for given parameter values there can be one or two asymptotically flat hairy black hole solutions in addition to the Schwarzschild solution. We analyze their perturbative stability and find that they can be stable or unstable, depending on the parameter values. The masses of stable hairy black holes that would be physically relevant range form stellar values up to values typical for supermassive black holes. One of their two metrics is extremely close to Schwarzschild, while all their “hair” is hidden in the second metric that is not coupled to matter and not directly seen. If the massive bigravity theory indeed describes physics, the hair of such black holes should manifest themselves in violent processes like black hole mergers and should be visible in the structure of the signals detected by LIGO/VIRGO.