In bacterial populations, cells are able to cooperate in order to yield complex collective functionalities. Interest in population-level cellular behaviour is increasing, due to both our expanding knowledge of the underlying biological principles, and the growing range of possible applications for engineered microbial consortia. Researchers in the field of synthetic biology - the application of engineering principles to living systems - have, for example, recently shown how useful decision-making circuits may be distributed across a bacterial population. The ability of cells to interact through small signalling molecules (a mechanism known as it quorum sensing) is the basis for the majority of existing engineered systems. However, horizontal gene transfer (or conjugation) offers the possibility of cells exchanging messages (using DNA) that are much more information-rich. The potential of engineering this conjugation mechanism to suit specific goals will guide future developments in this area. Motivated by a lack of computational models for examining the specific dynamics of conjugation, we present a simulation framework for its further study. We present an agent-based model for conjugation dynamics, with realistic handling of physical forces. Our framework combines the management of intercellular interactions together with simulation of intracellular genetic networks, to provide a general-purpose platform. We validate our simulations against existing experimental data, and then demonstrate how the emergent mixing patterns of multi-strain populations can affect conjugation dynamics. Our model of conjugation, based on a probability distribution, may be easily tuned to correspond to the behaviour of different cell types. Simulation code and movies are available at http://code.google.com/p/discus/.