Prompt learning is a popular fine-tuning method for vision-language models due to its efficiency. It requires a small number of additional learnable parameters while significantly enhancing performance on target tasks. However, most existing methods suffer from overfitting to fine-tuning data, yielding poor generalizability. To address this, we propose a new training objective function based on a Bayesian learning principle to balance adaptability and generalizability. We derive a prior over the logits, where the mean function is parameterized by the pre-trained model, while the posterior corresponds to the fine-tuned model. This objective establishes a balance by allowing the fine-tuned model to adapt to downstream tasks while remaining close to the pre-trained model. To avoid the overfitting issues of the standard softmax function, we adopt the one-vs-each softmax approximation along with its P\'olya-Gamma augmentation (OVE-PG). We evaluate our method on several benchmark datasets and demonstrate that using the Bayesian principle for prompt learning is indeed a sensible choice. Code is available at the https://github.com/ParkLabML/BayesianPrinciplesImprovePromptLearningInVisionLanguageModels.