If mutually mistrustful parties A and B control two or more appropriately located sites, special relativity can be used to guarantee that a pair of messages exchanged by A and B are independent. In earlier work we used this fact to define a relativistic bit commitment protocol, RBC1, in which security is maintained by exchanging a sequence of messages whose transmission rate increases exponentially in time. We define here a new relativistic protocol, RBC2, which requires only a constant transmission rate and could be practically implemented. We prove that RBC2 allows a bit commitment to be indefinitely maintained with unconditional security against all classical attacks. We examine its security against quantum attacks, and show that it is immune from the class of attacks shown by Mayers and Lo-Chau to render non-relativistic quantum bit commitment protocols insecure.