As one of the newly introduced resistive random access memory (ReRAM) devices, this paper has shown an in-depth study of conductive-bridging random access memory (CBRAM) for non-volatile memory (NVM) computing. Firstly, a CBRAM-crossbar based memory is evaluated with accurate physical-level model and circuit-level characterization. It is then deployed as NVM component with a 3D hybrid integration of SRAM/DRAM, where one layer of CBRAM-crossbar is designed for data-retention under power gating to reduce leakage power from SRAM/DRAM at other layers. Moreover, a block-level data-retention scheme is designed to only write back dirty data from SRAM/DRAM to CBRAM-crossbar. When compared to the hybrid memory using phase-change random access memory (PCRAM) as data-retention, our CBRAM-based hybrid memory achieves 16x faster migration time and 4x less migration power for hibernating transition. When compared to the FeRAM-based bit-wise data-retention, our approach also achieves 17x smaller area and 8x smaller power under the same data migration speed.