We use the bulge Sersic index n and bulge-to-total mass ratio (B/T) to explore the fundamental question of how bulges form. We perform two-dimensional bulge-disk-bar decomposition on H-band images of 143 bright, high-mass (M(*) >= 1.0 x 10(10) M(circle dot)) low-to-moderately inclined (i < 70 degrees) spirals. Our results are as follows. (1) Our H-band bar fraction (similar to 58%) is consistent with that from ellipse fits. (2) 70% of the stellar mass is in disks, 10% in bars, and 20% in bulges. (3) A large fraction (similar to 69%) of bright spirals have B/T <= 0.2, and similar to 76% have low n <= 2 bulges. These bulges exist in barred and unbarred galaxies across a wide range of Hubble types. (4) About 65% (68%) of bright spirals with n <= 2 (B/T <= 0.2) bulges host bars, suggesting a possible link between bars and bulges. (5) We compare the results with predictions from a set of ACDM models. In the models, a high-mass spiral can have a bulge with a present-day low B/T <= 0.2 only if it did not undergo a major merger since z <= 2. The predicted fraction (similar to 1.6%) of high-mass spirals, which have undergone a major merger since z <= 4 and host a bulge with a present-day low B/T <= 0.2, is a factor of over 30 smaller than the observed fraction (similar to 66%) of high-mass spirals with B/T <= 0.2. Thus, contrary to common perception, bulges built via major mergers since z <= 4 seriously fail to account for the bulges present in similar to 66% of high mass spirals. Most of these present-day low B/T <= 0.2 bulges are likely to have been built by a combination of minor mergers and/or secular processes since z <= 4.