Two models are proposed to predict the evolution of shear band width as a function of applied strain for simulated glasses mechanically deformed in simple shear. The first model arises from dimensional analysis and an assumption that band broadening is controlled by the strain rate inside the shear band. The second model describes the shear band as a pulled front propagating into an unsteady state, the dynamics of which are described using the effective temperature shear transformation zone (ET-STZ) theory. Both models are compared to three simulated systems: a two-dimensional binary Lennard-Jones glass, a Cu64Zr36 glass modeled using an embedded atom method (EAM) potential, and a Si glass modeled using the Stillinger-Weber potential. Shear bands form in all systems across a variety of quench rates. Depending on the case these bands either appear to broaden indefinitely or to saturate to a finite width. The shear band strain rate model appears to apply only when band growth is unconstrained, indicating the dominance of a single time scale in the early stages of band development. The front propagation model, which reduces to the other model in the early stages of band broadening, also applies to cases in which the band width saturates, suggesting that competition between the rate of shear-induced configurational disordering and thermal relaxation set a maximum width for shear bands in a variety of materials systems.