Reionization is an inhomogeneous process, thought to begin in small ionized bubbles of the intergalactic medium (IGM) around overdense regions of galaxies. Recent Ly alpha studies during the epoch of reionization show evidence that ionized bubbles formed earlier around brighter galaxies, suggesting higher IGM transmission of Ly alpha from these galaxies. We investigate this problem using IR slitless spectroscopy from the Hubble Space Telescope (HST) Wide-Field Camera 3 (WFC3) G102 grism observations of 148 galaxies selected via photometric redshifts at 6.0 < z < 8.2. These galaxies have spectra extracted from the CANDELS Ly alpha Emission at Reionization (CLEAR) survey. We combine the CLEAR data for 275 galaxies with the Keck Deep Imaging Multi-Object Spectrograph and MOSFIRE data set from the Texas Spectroscopic Search for Ly alpha Emission at the End of Reionization Survey. We constrain the Ly alpha equivalent width (EW) distribution at 6.0 < z < 8.2, which is described by an exponential form, dN/dEW proportional to exp(-EW) W-0, with the characteristic e-folding scale width (W-0). We confirm a significant drop in the Ly alpha strength (i.e., W-0) at z > 6. Furthermore, we compare the redshift evolution of W-0 between galaxies at different UV luminosities. UV-bright (M-UV < -21 [i.e., L-UV > L*]) galaxies show weaker evolution with a decrease of 0.4 (+/- 0.2) dex in W-0 at z > 6, while UV-faint (M-UV > -21 [L-UV < L*]) galaxies exhibit a significant drop of 0.7-0.8 (+/- 0.2) dex in W-0 from z < 6 to z > 6. If the change in W-0 is proportional to the change in the IGM transmission for Ly alpha photons, then this is evidence that the transmission is "boosted" around UV-brighter galaxies, suggesting that reionization proceeds faster in regions around such galaxies.