We explore the relationship between X-ray absorption and optical obscuration within the BAT AGN Spectroscopic Survey (BASS) which has been collecting and analyzing the optical and X-ray spectra for 641 hard X-ray selected ($E>14$ keV) active galactic nuclei (AGN). We use the deviation from a linear broad H$alpha$-to-X-ray relationship as an estimate of the maximum optical obscuration towards the broad line region and compare the $A_{rm V}$ to the hydrogen column densities ($N_{rm H}$) found through systematic modeling of their X-ray spectra. We find that the inferred columns implied by $A_{rm V}$ towards the broad line region (BLR) are often orders of magnitude less than the columns measured towards the X-ray emitting region indicating a small scale origin for the X-ray absorbing gas. After removing 30% of Sy 1.9s that potentially have been misclassified due to outflows, we find that 86% (164/190) of the Type 1 population (Sy 1--1.9) are X-ray unabsorbed as expected based on a single obscuring structure. However, 14% (26/190), of which 70% (18/26) are classified as Sy 1.9, are X-ray absorbed, suggesting the broad line region itself is providing extra obscuration towards the X-ray corona. The fraction of X-ray absorbed Type 1 AGN remains relatively constant with AGN luminosity and Eddington ratio, indicating a stable broad line region covering fraction.