Semiconductor ring lasers (SRLs) are currently being actively investigated because of their possible applications in photonic integrated circuits. Some SRLs exhibit bistable operation, suggesting their possible use as e.g. all-optical memories. We have reduced a basic rate equation model for the counter-propagating fields in these SRLs to a two-dimensional system by applying asymptotic techniques. Studying the deterministic and stochastic switching properties in this reduced phase space greatly enhances our physical understanding of the dynamical behaviour of these SRLs.