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Due to its flexibility and low cost, the bistatic forward-looking synthetic aperture radar (BFSAR) which employs side-looking transmitter and forward-looking receiver has been studied in recent years. Sparsity-based techniques have been applied in the field of BFSAR imaging and show great potential. In sparsity-based BFSAR imaging, compensation of the motion errors is crucial to get a well-focused image. For fields that admit a sparse representation, we propose a sparsity-based imaging approach integrated with motion error estimation and compensation in this paper. First, a novel joint phase-amplitude compensation-based motion error correction scheme is developed to cope with the spatial variance of motion error. Then, an inversion observation model of the range-Doppler algorithm combined with motion error correction is derived, based on which a joint problem of BFSAR imaging and motion error estimation is formulated as a sparse recovery problem and solved in an iterative way, where in each iteration, both image formation and motion error correction are carried out. Experiments on both the simulated and real BFSAR data show that the proposed method can obtain a more accurate estimation result, and generate better focused images compared with the existing methods.