The relative viscosity (mrel=suspension viscosity/suspending fluid viscosity) of low Reynolds number, dilute, surfactant-free bubble suspensions in simple shear is studied with a rotating cylinder Couette rheometer. The conditions of the experiments correspond to capillary numbers (Ca) of order 1 and bridge previous experimental, theoretical and numerical results that focussed on either Ca<<1 or Ca>>1. The suspensions are shear thinning with mrel >1 for small Ca. At large Ca, mrel approaches a constant that is less than 1. These results are explained by a scaling analysis that considers how regions of viscous dissipation in and around bubbles change as bubbles are deformed by the flow.