The availability of protein is an important factor for the determination of the size of the mitotic spindle. Involved in spindle-size regulation is kinesin-8, a molecular motor and microtubule (MT) depolymerase, which is known to tightly control MT length. Here, we propose and analyze a theoretical model in which kinesin-induced MT depolymerization competes with spontaneous polymerization while supplies of both tubulin and kinesin are limited. In contrast to previous studies where resources were unconstrained, we find that, for a wide range of concentrations, MT length regulation is bistable. We test our predictions by conducting in vitro experiments and find that the bistable behavior manifests in a bimodal MT length distribution.