We present an optical transmission spectrum of the atmosphere of WASP-4b obtained through observations of four transits with Magellan/IMACS, as part of the Arizona-CfA-Católica-Carnegie Exoplanet Spectroscopy Survey (ACCESS). Using a Bayesian approach to atmospheric retrieval, we find no evidence for scattering or absorption features in our transit spectrum. Our models include a component to model the transit light source effect (spectral contamination from unocculted spots on the stellar photosphere), which we show can have a marked impact on the observed transmission spectrum for reasonable spot-covering fractions (<5%); this is the first such analysis for WASP-4b. We are also able to fit for the size and temperature contrast of spots observed during the second and third transits, finding evidence for both small, cool and large, warm spot-like features on the photosphere. Finally, we compare our results to those published by Huitson et al. using Gemini/GMOS and May et al. using IMACS, and we find that our data are in agreement.