We propose a 6D Bayesian-based localization framework to estimate the position and rotation angles of a mobile station (MS) within an indoor reconfigurable intelligent surface (RIS)-aided system. This framework relies on a probabilistic graphical model to represent the joint probability distribution of random variables through their conditional dependencies and employs the No-U-Turn Sampler (NUTS) to approximate the posterior distribution based on the estimated channel parameters. Our framework estimates both the position and rotation of the mobile station (MS), in the presence of channel parameter estimation errors. We derive the Cramer-Rao lower bound (CRLB) for the proposed scenario and use it to evaluate the system's position error bound (PEB) and rotation error bound (REB). We compare the system performances with and without RIS. The results demonstrate that the RIS can enhance positioning accuracy significantly.