The relative viscosity (mu(rel) = suspension viscosity/suspending fluid viscosity) of low Reynolds number, dilute and 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 I and bridge previous experimental, theoretical and numerical results that focused on either Ca much less than 1 or Ca much greater than 1. The suspensions are shear thinning with mu(rel) > 1 for small Ca. At large Ca, mu(rel) 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.