Passive bistatic radar (PBR) systems use existing RF broadcast and communication signals in the environment for surveillance and tracking applications. GSM mobile communication signal based PBR systems are suitable for short range surveillance systems, but the low-bandwidth of the signal results in low range resolutions when classical cross-correlation based processing is used for target detection. An alternative and more robust approach based on compressive sensing (CS) is proposed here to achieve high range resolution by performing fine gridding for the target scene. To avoid the increased coherence and computational load associated with the fine gridding, pre-processing steps are introduced in this paper, which involve choosing a suitable CS basis by application of spectral and subspace transformations. By so doing, resolution improvement is achieved when a single channel GSM signal and CS are employed for target detection.