This paper considers the input design of kernel-based regularization methods for LTI system identification. We first derive the Bayesian mean squared error matrix under the Bayesian perspective, and then use some typical scalar measures (e.g., the A-optimality, D-optimality, and E-optimality) as optimization criteria for the input design problem. Instead of directly solving the nonconvex optimization problem, we propose a two-step procedure. The first step is to solve a convex optimization and the second one is to determine the inverse image of a quadratic map. Both of these two steps can be solved efficiently by the proposed method and hence all the globally optimal inputs are found. In particular, we show that for some kernels, the optimal input under the D-optimality has an explicit expression.