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We study numerically the hydrodynamics of an active polar suspension, both in the absence and in the presence of an external shear. We focus on extensile fluids, which are models for bacterial suspensions and are well known to undergo a transition from a quiescent to a spontaneously flowing state, even in one dimension. We characterise the transition to spontaneous flow in a quasi-2-dimensional geometry. We find that it is continuous, and that the succession of steady states obtained for an extensile fluid are dramatically different when the orientation, or polarisation, field is fully two-dimensional or when it is allowed to move out of the plane. Shear slightly stabilises the passive phase and strongly affects the accessible steady states. The distinction between polar active fluids of 'mover' and 'shaker' particles (with and without self-advection, respectively) is addressed; we find that density inhomogeneities are greatly enhanced by self-advection.