Large language models (LLMs) showcase many desirable traits for intelligent and helpful robots. However, they are also known to hallucinate predictions. This issue is exacerbated in robotics where LLM hallucinations may result in robots confidently executing plans that are contrary to user goals or relying more frequently on human assistance. In this work, we present LBAP, a novel approach for utilizing off-the-shelf LLMs, alongside Bayesian inference for uncertainty Alignment in robotic Planners that minimizes hallucinations and human intervention. Our key finding is that we can use Bayesian inference to more accurately calibrate a robots confidence measure through accounting for both scene grounding and world knowledge. This process allows us to mitigate hallucinations and better align the LLM's confidence measure with the probability of success. Through experiments in both simulation and the real world on tasks with a variety of ambiguities, we show that LBAP significantly increases success rate and decreases the amount of human intervention required relative to prior art. For example, in our real-world testing paradigm, LBAP decreases the human help rate of previous methods by over 33% at a success rate of 70%.