Dynamic searchable symmetric encryption has attracted much attention because it allows users to securely search and dynamically update encrypted documents stored in a semi-trusted cloud server. However, most searchable symmetric encryption schemes only support single-keyword search, failing to achieve conjunctive search while protecting forward and backward privacy. In addition, most schemes are not robust, which means that they cannot handle irrational update requests from a client, such as adding or deleting a certain keyword/file identifier pair, or deleting non-existent keywords/file identifier pairs. To address these challenges, this study proposes a robust scheme for conjunctive dynamic symmetric searchable encryption that preserves both forward and backward privacy, called RFBC. In this scheme, the server constructs two Bloom filters for each keyword, which are used to store the relevant hash values of the keyword/file identifier pair to be added and deleted, respectively. When the client sends update requests, the server uses the two Bloom filters to determine and filter irrational update requests, so as to guarantee the robustness of the scheme. In addition, by combining the status information of the lowest frequency keywords among multiple keywords, the Bloom filters, and the update counter, RFBC realizes conjunctive search by filtering out file identifiers that do not contain the rest keywords. Finally, by defining the leakage function, RFBC is proved to be forward private and Type-III backward private through a series of security analyses. Experimental results show that compared with related schemes, RFBC greatly improves computation and communication efficiency. Specifically, the computational overhead of update operations in RFBC is about 28% and 61.7% of that in ODXT and BDXT, respectively. The computational overhead of search operations in RFBC is about 21.9% and 27.3% of that in ODXT and BDXT, respectively. The communication overhead of search operations in RFBC is about 19.7% and 31.6% of that in ODXT and BDXT, respectively. Moreover, as the proportion of irrational updates gradually increases, RFBC exhibits significantly higher improvement in search efficiency compared to both BDXT and ODXT.