The topic of power conversion limits for size-constrained kinetic energy harvesting systems, and the associated optimal design, has mainly been explored for monochromatic and stochastic excitations. In this work, we present a first extension where we evaluate the absolute power conversion bound in the case of bi-chromatic vibration inputs. The resulting maximum power limit is shown to depend on both the relative amplitude and the phase shift of the input harmonics. We then evaluate this bound numerically for a near-optimally matched velocity-damped resonant generator. We show that for some relative amplitudes and phase shifts of the input vibration harmonics, the converted power drops to 45% of the absolute power bound, well below the well-known 79% limit that holds for monochromatic inputs.