Privacy preservation in opportunistic networks, such as disruption and delay tolerant networks, constitutes a very challenging area of research. The wireless channel is vulnerable to malicious nodes that can eavesdrop data exchanges. Moreover, all nodes in an opportunistic network can act as routers and thus, gain access to sensitive information while forwarding data. Node anonymity and data protection can be achieved using encryption. However, cryptography-based mechanisms are complex to handle and computationally expensive for the participating (mobile) nodes. We propose SimBet-BF, a privacy-preserving routing algorithm for opportunistic networks. The proposed algorithm builds atop the SimBet algorithm and uses Bloom filters so as to represent routing as well as other sensitive information included in data packets. SimBet-BF provides anonymous communication and avoids expensive cryptographic operations, while the functionality of the SimBet algorithm is not significantly affected. In fact, we show that the required security level can be achieved with a negligible routing performance trade-off.