We present a new ground-based visual transmission spectrum of the hot Jupiter WASP-43b, obtained as part of the ACCESS Survey. The spectrum was derived from four transits observed between 2015 and 2018, with combined wavelength coverage between 5300 and 9000 and an average photometric precision of 708 ppm in 230 bins. We perform an atmospheric retrieval of our transmission spectrum combined with literature Hubble Space Telescope/WFC3 observations to search for the presence of clouds/hazes as well as Na, K, Hα, and H2O planetary absorption and stellar spot contamination over a combined spectral range of 5318-16420. We do not detect a statistically significant presence of Na i or K i alkali lines, or Hα in the atmosphere of WASP-43b. We find that the observed transmission spectrum can be best explained by a combination of heterogeneities on the photosphere of the host star and a clear planetary atmosphere with H2O. This model yields a log evidence of 8.26 ± 0.42 higher than a flat (featureless) spectrum. In particular, the observations marginally favor the presence of large, low-contrast spots over the four ACCESS transit epochs with an average covering fraction fhet=0.27-0.16+0.42 and temperature contrast ΔT = 132 K ± 132 K. Within the planet's atmosphere, we recover a log H2O volume mixing ratio of -2.78-1.47+1.38, which is consistent with previous H2O abundance determinations for this planet.