The existence of bulk nanobubbles has long been regarded with scepticism, due to the limitations of experimental techniques and the widespread assumption that spherical bubbles cannot achieve stable equilibrium. We develop a model for the stability of bulk nanobubbles based on the experimental observation that the zeta potential of spherical bubbles abruptly diverges from the planar value below 10μm. Our calculations recover three persistently reported—but disputed—properties of bulk nanobubbles: that they stabilize at a typical radius of ∼100nm, that this radius is bounded below 1 μm, and that it increases with ionic concentration.