Suspending self-propelled “pushers” in a liquid lowers its viscosity. We study how this phenomenon depends on system size in bacterial suspensions using bulk rheometry and particle-tracking rheoimaging. Above the critical bacterial volume fraction needed to decrease the viscosity to zero, ϕ c ≈ 0.75 % , large-scale collective motion emerges in the quiescent state, and the flow becomes nonlinear. We confirm a theoretical prediction that such instability should be suppressed by confinement. Our results also show that a recent application of active liquid-crystal theory to such systems is untenable.