The Bi1-xCaxMnO3 system is known to exhibit charge ordering for a much broader range of x than the La1-xCaxMnO3 system. However, the properties of Bi1-xCaxMnO3 over the entire doping range are not well understood. We have performed magnetization and resistivity measurements as well as x-ray absorption and x-ray diffraction measurements on Bi1-xCaxMnO3 to correlate structural, magnetic, and transport properties. The system is insulating and antiferromagnetic for the entire range of x studied (x>=0.4) except near x~0.9, where we find a canted spin arrangement with approximately one Bohr magneton per Mn site. Detailed magnetization measurements were performed as a function of field and temperature to explore the net moment on the Mn sites as a function of x and reveal the charge ordering and Néel temperatures. X-ray absorption measurements reveal significant structural distortions of the Mn-O bond distributions with increasing Bi content that correlates directly with increasing charge-ordering temperatures. Moreover, the x-ray diffraction data reveal peak splittings consistent with lower-symmetry cells as Bi content increases. These structural-magnetic correlations point to the importance of Mn-O distortions in stabilizing the charge-ordered state in the manganites.