We consider the problem of convolutive blind source separation of stereo mixtures, where a pair of microphones records mixtures of sound sources that are convolved with the impulse response between each source and sensor. We propose an Adaptive Stereo Basis (ASB) source separation method for such convolutive mixtures, using an adaptive transform basis which is learned from the stereo mixture pair. The stereo basis vector pairs of the transform are grouped according to the estimated relative delay between the left and right channels for each basis, and the sources are then extracted by projecting the transformed signal onto the subspace corresponding to each group of basis vector pairs. The performance of the proposed algorithm is compared with FD-ICA and DUET under different reverberation and noise conditions, using both objective distortion measures and formal listening tests.