Bayesian inference is an effective approach for solving statistical learning problems, especially with uncertainty and incompleteness. However, Bayesian inference is a computing-intensive task whose efficiency is physically limited by the bottlenecks of conventional computing platforms. In this paper, a spintronics-based stochastic computing (SC) approach is proposed for efficient Bayesian inference. The inherent stochastic switching behaviors of spintronic devices are exploited to build a stochastic bitstream generator (SBG) for SC with hybrid CMOS/magnetic tunnel junction (MTJ) circuits design. Aiming to improve the inference efficiency, an SBG sharing strategy is leveraged to reduce the required SBG array scale by integrating a switch network between SBG array and SC logic. A device-to-architecture level framework is proposed to evaluate the performance of spintronics-based Bayesian inference system (SPINBIS). Experimental results on data fusion applications have shown that SPINBIS could improve the energy efficiency about 12× than MTJ-based approach with 45% design area overhead and about 26× than FPGA-based approach.