We present a study of large-scale bars in the local universe, based on a large sample of 3692 galaxies, with 18.5 <= M-g < -22.0 mag and redshift 0.01 <= z < 0.03, drawn from the Sloan Digitized Sky Survey. Our sample includes many galaxies that are disk-dominated and of late Hubble types. Both color cuts and Se e rsic cuts yield a similar sample of similar to 2000 disk galaxies. We characterize bars and disks by ellipse-fitting r-band images and applying quantitative criteria. After excluding highly inclined (60 degrees) systems, we find the following results. (1) The optical r-band fraction (f(opt-r)) of barred galaxies, when averaged over the whole sample, is similar to 48%-52%. (2) When galaxies are separated according to half light radius (r(e)), or normalized r(e)/R-24, which is a measure of the bulge-to-disk (B/D) ratio, a remarkable result is seen: f(opt-r) rises sharply, from similar to 40% in galaxies that have small r(e)/R-24 and visually appear to host prominent bulges, to similar to 70% for galaxies that have large r(e)/R-24 and appear disk-dominated. (3) For galaxies with bluer colors, f(opt-r) rises significantly (by similar to 30%). A weaker rise (by similar to 15%-20%) is seen for lower luminosities or lower masses. (4) While hierarchical Lambda CDM models of galaxy evolution models fail to produce galaxies without classical bulges, our study finds that similar to 20% of disk galaxies appear to be "quasi-bulgeless.'' (5) We outline how the effect of a decreasing resolution and a rising obscuration of bars by gas and dust over z = 0.2-1.0 can cause a significant artificial loss of bars, and an artificial reduction in the optical bar fraction over z = 0.2-1.0.