We present a study of the bar fraction in the Coma Cluster galaxies based on a sample of ~190 galaxies selected from the Sloan Digital Sky Survey Data Release 6 and observed with the Hubble Space Telescope (HST) Advanced Camera for Survey (ACS). The unprecedented resolution of the HST-ACS images allows us to explore the presence of bars, detected by visual classification, throughout a luminosity range of 9 mag (-23 <~ Mr <~ -14), permitting us to study the poor known region of dwarf galaxies. We find that bars are hosted by galaxies in a tight range of both luminosities (-22 <~ Mr <~ -17) and masses (10^{9} ≲ M_{*}}/{M}_{&sun;} ≲ 10^{11}). This result holds when compared with a sample of bright/massive field galaxies. In addition, we find that the bar fraction does not vary significantly when going from the center to the cluster outskirts, implying that cluster environment plays a second-order role in bar formation/evolution. The shape of the bar fraction distribution with respect to both luminosity and mass is well matched by the luminosity distribution of disk galaxies in Coma, indicating that bars are good tracers of cold stellar disks. We discuss the implications of our results for the formation and evolution scenarios of bars and disks.