Symbolic regression aims to discover concise, interpretable mathematical expressions that satisfy desired objectives, such as fitting data, posing a highly combinatorial optimization problem. While genetic programming has been the dominant approach, recent efforts have explored reinforcement learning methods for improving search efficiency. Monte Carlo Tree Search (MCTS), with its ability to balance exploration and exploitation through guided search, has emerged as a promising technique for symbolic expression discovery. However, its traditional bandit strategies and sequential symbol construction often limit performance. In this work, we propose an improved MCTS framework for symbolic regression that addresses these limitations through two key innovations: (1) an extreme bandit allocation strategy tailored for identifying globally optimal expressions, with finite-time performance guarantees under polynomial reward decay assumptions; and (2) evolution-inspired state-jumping actions such as mutation and crossover, which enable non-local transitions to promising regions of the search space. These state-jumping actions also reshape the reward landscape during the search process, improving both robustness and efficiency. We conduct a thorough numerical study to the impact of these improvements and benchmark our approach against existing symbolic regression methods on a variety of datasets, including both ground-truth and black-box datasets. Our approach achieves competitive performance with state-of-the-art libraries in terms of recovery rate, attains favorable positions on the Pareto frontier of accuracy versus model complexity.