We study the effect of optical squeezing on the performance of a sensitive, quantum-noise-limited optically-pumped magnetometer. We use Bell-Bloom optical pumping to excite a $^{87}$Rb vapor and Faraday rotation to detect spin precession. The sub-$mathrm{pT}/sqrt{mathrm{Hz}}$ sensitivity is limited by spin projection noise (photon shot noise) at low (high) frequencies. Probe polarization squeezing both improves high-frequency sensitivity and increases signal bandwidth. The accompanying polarization anti-squeezing perturbs only an unmeasured spin component, so there is no loss of sensitivity at any frequency. The method is compatible with high-density and multi-pass techniques that reach extreme sensitivity.