As part of the Advanced Camera for Surveys (ACS) Virgo Cluster Survey, we have measured surface brightness fluctuations (SBFs) in a sample of 100 early-type Virgo galaxies. Distances derived from these measurements are needed to explore the three-dimensional structure of the Virgo Cluster, study the intrinsic parameters of globular clusters associated with the program galaxies, and compare with the galaxy distances derived from globular cluster luminosity functions. Our SBF measurements have been performed in the F850LP bandpass of the Wide Field Channel of the ACS on the Bubble Space Telescope. These are the first measurements of this kind, and we present the first SBF calibration for this bandpass. The measured fluctuations depend on galaxy stellar population variations, which we quantify by galaxy color (g475 - z 850)0, where g475 and z850 are the galaxy magnitudes in the F475W and F850LP ACS filters, respectively. We derive the calibration for the absolute SBF magnitude M̄850 = - 2.06 ± 0.04 + (2.0 ± 0.2)[(g475 - z850) 0 - 1.3] in the range 1.3 < (g475 - z 850)0 ≤ 1.6, and M̄850 = -2.06 ± 0.04 + (0.9 ± 0.2)[(g415 - z850)0 - 1.3] in the range 1.0 < (g415 - z850)0 ≤ 1.3. The quoted zero-point uncertainty here includes all sources of internal error; there is an additional systematic uncertainty of ∼0.15 mag, due to the uncertainty in the distance scale calibration. Physically, the two different color regimes correspond to different galaxy types: giant ellipticals and S0s at the red end, and early-type dwarfs at the blue end. For the first time in SBF studies, we are able to provide a firm empirical calibration of SBF in early-type dwarf galaxies. Our results agree with stellar population model predictions from Bruzual & Chariot in the range 1.3 < (g475 - z850)0 ≤ 1.6, while our empirical slope is somewhat steeper than the theoretical prediction in the range 0.9 ≤ (g475 - z850)0 ≤ 1.3.