As an important branch of embodied artificial intelligence, mobile manipulators are increasingly applied in intelligent services, but their redundant degrees of freedom also limit efficient motion planning in cluttered environments. To address this issue, this paper proposes a hybrid learning and optimization framework for reactive whole-body motion planning of mobile manipulators. We develop the Bayesian distributional soft actor-critic (Bayes-DSAC) algorithm to improve the quality of value estimation and the convergence performance of the learning. Additionally, we introduce a quadratic programming method constrained by the signed distance field to enhance the safety of the obstacle avoidance motion. We conduct experiments and make comparison with standard benchmark. The experimental results verify that our proposed framework significantly improves the efficiency of reactive whole-body motion planning, reduces the planning time, and improves the success rate of motion planning. Additionally, the proposed reinforcement learning method ensures a rapid learning process in the whole-body planning task. The novel framework allows mobile manipulators to adapt to complex environments more safely and efficiently.