We describe hydrodynamic models of bipolar outbursts in recurrent nova systems containing a red giant with a dense wind. Two mechanisms are investigated for the production of the bipolarity observed in the outbursts of some such systems - a model in which the outburst occurs as a point explosion in an anisotropic wind, and one in which the wind is isotropic but the outburst itself is intrinsically bipolar. It is argued on the basis of radio observations of RS Oph (1985) that the latter model is more likely to be appropriate. The numerical computations of bipolar explosions also show that the ejection of parcels of gas at highly supersonic, and oppositely directed, velocities into a dense surrounding medium gives rise to bowshocks which interact in such a way as to give a dense ring of material in a plane normal to the line of ejection.