Image captioning offers a computational process to understand the semantics of images and convey them using descriptive language. However, automated captioning models may not always generate satisfactory captions due to the complex nature of the images and the quality/size of the training data. We propose an interactive captioning framework to improve machine-generated captions by keeping humans in the loop and performing an online-offline knowledge acquisition (KA) process. In particular, online KA accepts a list of keywords specified by human users and fuses them with the image features to generate a readable sentence that captures the semantics of the image. It leverages a multimodal conditioned caption completion mechanism to ensure the appearance of all user-input keywords in the generated caption. Offline KA further learns from the user inputs to update the model and benefits caption generation for unseen images in the future. It is built upon a Bayesian transformer architecture that dynamically allocates neural resources and supports uncertainty-aware model updates to mitigate overfitting. Our theoretical analysis also proves that Offline KA automatically selects the best model capacity to accommodate the newly acquired knowledge. Experiments on real-world data demonstrate the effectiveness of the proposed framework.