We present new Brownian dynamics techniques for studying blockers of ion channels. By treating the channel as a fixed body, simulating the blocker molecules using rigid bodies, and using an implicit water force field with explicit ions, we are able to carry out fast simulations that can be used to investigate the dynamics of block and unblock, deduce binding modes, and calculate binding affinities. We test our program using the NavAb bacterial sodium channel, whose structure was recently solved (Payandeh et al. Nature, 2011, 47.5, 353-358) in conjunction with the mu-conotoxin PIIIA blocker. We derive an ohmic current-voltage relationship for channel permeation, calculate potentials of mean force for blocker unbinding, and deduce multiple binding modes for the blocker. Our results are shown to be compatible with other computational and experimental results. Finally, we discuss future improvements such as the inclusion of flexible side chains. After these improvements are carried out, we anticipate our program will be an extremely useful new tool that could be used to help develop new drugs to treat a range of ion-channel related diseases.