Source localization with sensor arrays is an active research topic in many areas, such as speaker localization and communication. The existing estimators usually focus on arrays with omnidirectional sensors, but struggle on arrays with directional sensors. In this work, a new method is proposed for locating the near-field sources based on sparse Bayesian learning (SBL), which is capable of integrating the near-field signal model to jointly estimate direction-of-arrival (DOA) and distance. By further considering the directionality of sensors in the signal model which takes full advantage of the magnitude information, the proposed method can handle arrays with both omnidirectional and directional sensors. Simulation results show that the proposed method yields a sharp spatial spectrum, and performs more accurately than traditional near-field Multiple Signal Classification (MUSIC) and Steered-Response Power Phase Transform (SRP-PHAT) for arrays covering heterogeneous directional sensors.