The current work introduces a novel combination of two Bayesian tools, Gaussian Processes (GPs), and the use of the Approximate Bayesian Computation (ABC) algorithm for kernel selection and parameter estimation for machine learning applications. The combined methodology that this research article proposes and investigates offers the possibility to use different metrics and summary statistics of the kernels used for Bayesian regression. The presented work moves a step toward online, robust, consistent, and automated mechanism to formulate optimal kernels (or even mean functions) and their hyperparameters simultaneously offering confidence evaluation when these tools are used for mathematical or engineering problems such as structural health monitoring (SHM) and system identification (SI).