Recently, several promising approximate message passing (AMP) based algorithms have been developed for bilinear recovery with model Y = K k=1 b k A k C + W , where {b k } and C are jointly recovered with known A k from the noisy measurements Y . The bilinear recover problem has many applications such as dictionary learning, self-calibration, compressive sensing with matrix uncertainty, etc. In this work, we propose a new bilinear recovery algorithm based on AMP with unitary transformation and hybrid message passing. It is shown that, compared to the state-of-the-art message passing based algorithms, the proposed algorithm is much more robust and faster, leading to remarkably better performance.