Roman's Galactic Bulge Time Domain Survey (GBTDS) will be an astrometry machine. The GBTDS will produce precise astrometry at an unprecedented temporal sampling for a large number of sources that both rivals and complements Gaia. I will discuss how GBTDS astrometry can be used to search for and characterize the Galaxy's population of non-interacting black holes via gravitational microlensing and reflex motion.