Knowledge-based Visual Question Answering (VQA) requires models to incorporate external knowledge to respond to questions about visual content. Previous methods mostly follow the "retrieve and generate" paradigm. Initially, they utilize a pre-trained retriever to fetch relevant knowledge documents, subsequently employing them to generate answers. While these methods have demonstrated commendable performance in the task, they possess limitations: (1) they employ an independent retriever to acquire knowledge solely based on the similarity between the query and knowledge embeddings, without assessing whether the knowledge document is truly conducive to helping answer the question; (2) they convert the image into text and then conduct retrieval and answering in natural language space, which may not ensure comprehensive acquisition of all image information. To address these limitations, we propose Boter, a novel framework designed to bootstrap knowledge selection and question answering by leveraging the robust multimodal perception capabilities of the Multimodal Large Language Model (MLLM). The framework consists of two modules: Selector and Answerer, where both are initialized by the MLLM and parameter-efficiently finetuned in a simple cycle: find key knowledge in the retrieved knowledge documents using the Selector, and then use them to finetune the Answerer to predict answers; obtain the pseudo-labels of key knowledge documents based on the predictions of the Answerer and weak supervision labels, and then finetune the Selector to select key knowledge; repeat. Our framework significantly enhances the performance of the baseline on the challenging open-domain Knowledge-based VQA benchmark, OK-VQA, achieving a state-of-the-art accuracy of 62.83%.