Recent interpretations of narrow, variable absorption lines detected in some Type Ia supernovae suggest that their progenitors are surrounded by dense, circumstellar material. Similar variations detected in the symbiotic recurrent nova system RS Oph, which undergoes thermonuclear outbursts every ~20 years, making it an ideal candidate to investigate the origin of these lines. To this end, we present simulations of multiple mass transfer-nova cycles in RS Oph. We find that the quiescent mass transfer produces a dense, equatorial outflow, i.e., concentrated towards the binary orbital plane, and an accretion disc forms around the white dwarf. The interaction of a spherical nova outburst with these aspherical circumstellar structures produces a bipolar outflow, similar to that seen in HST imaging of the 2006 outburst. In order to produce an ionization structure that is consistent with observations, a mass-loss rate of $5\times 10-7M\odot \mathrm{yr}-1$ from the red giant is required. The simulations also produce a polar accretion flow, which may explain the broad wings of the quiescent H {\alpha} line and hard X-rays. By comparing simulated absorption line profiles to observations of the 2006 outburst, we are able to determine which components arise in the wind and which are due to the novae. We explore the possible behaviour of absorption line profiles as they may appear should a supernova occur in a system like RS Oph. Our models show similarities to supernovae like SN 2006X, but require a high mass-loss rate, $M\dot{}\sim 10-6$ to $10-5M\odot \mathrm{yr}-1$, to explain the variability in SN 2006X.