To address the shortcomings of existing bearing remaining useful life (RUL) prediction process such as low accuracy and reliance on expert experience for parameter estimation, this paper proposes a bearing RUL prediction method combining relevance vector machine (RVM) and hybrid degradation model. The bearing degradation characteristics are extracted from the acquired vibration acceleration signals, the time-varying $3\sigma$ criterion is then used to determine the bearing first predicting time (FPT), and the sequence from initial failure time point to the inspection time is regressed by differential kernel parameter RVM to obtain the different sparse relevance vectors (RVs). A mixed degenerate model combined single exponential, weighted double exponential, and polynomial is used to fit the sparse RVs to obtain the fitted curve clusters. The similarity based on bidirectional Hausdorff distance (BHD) is used to select the best degradation curve, and to extrapolate the best degradation curve to the failure threshold (FT). The experimental results indicate that the proposed method overcomes the widespread drawbacks of monotonicity and trend bias in model-based methods, and has better prediction efficiency than the conventional exponential models.