In microbubble (MB) cavitation-mediated blood-brain barrier (BBB) opening, prior knowledge of the skull's sound speed properties is required to correct phase aberration and achieve accurate localization of the cavitation source using transcranial passive acoustic mapping (TPAM). Current approaches predominantly rely on CT scans to generate an empirical sound speed map (SSM) for correction after registering the two imaging modalities. This increases hardware complexity and cost while introducing additional errors from the registration process and the empirical sound speed values in the SSM. Here, we propose an all-ultrasound, single-probe method for refraction-corrected TPAM. This method firstly deploys the head wave technique to reconstruct an approximate multi-layer SSM of the skull. This SSM is then combined with the heterogeneous angular spectrum approach for PAM to efficiently reconstruct refraction-corrected TPAM images. In the in-vitro hydrophone and MB cavitation experiments using two whole macaque calvariae, we showed that the source localization error could be reduced to a sub-millimeter scale with the proposed method in the area where the F-number is less than 1.2. Compared to the cases without phase aberration correction, the localization error was reduced by about 1.8 - 5.9 times in the corrected cases, clearly demonstrating the effectiveness of the proposed method for transcranial acoustic source localization. We also showed that the proposed method achieved comparable performance on correcting source localization to the CT-corrected method. These preliminary results suggest that our method represents a low-cost solution for monitoring transcranial MB cavitation activity, particularly in the cortical regions, which could facilitate the investigation of MB-mediated focused therapies in the brain and warrants further study for clinical translation.