Searchable Symmetric Encryption (SSE), which enables users to search over encrypted data without decryption, has gained increasing attention from both academic and industrial fields. However, existing SSE schemes either have low search efficiency or cannot support multi-keyword search, dynamic updates, and result verification simultaneously. To solve these problems, we propose a Verifiable and Dynamic Multi-keyword Search (VDMS) scheme over encrypted data by using the bitmap and RSA accumulator, which provides multi-keyword search over encrypted data in an efficient, verifiable and updated way. The bitmap is used as a data structure to build the indexes, which improves the search efficiency and reduces the storage space of the indexes. The RSA accumulator and bitmap are combined to verify the correctness of results. Formal security analysis proves that our VDMS is adaptively secure against Chosen-Keyword Attacks (CKA), and empirical experiments using a real-world dataset demonstrate that our VDMS is efficient and feasible in practical applications.