We present the relation between stellar specific angular momentum j(*), stellar mass M-*, and bulge-to-total light ratio beta for The H I Nearby Galaxy Survey, the Calar Alto Legacy Integral Field Area Survey, and Romanowsky & Fall data sets, exploring the existence of a fundamental plane between these parameters, as first suggested by Obreschkow & Glazebrook. Our best-fit M-*-j(*) relation yields a slope of alpha = 1.03 +/- 0.11 with a trivariate fit including beta. When ignoring the effect of beta, the exponent alpha = 0.56 +/- 0.06 is consistent with alpha = 2/3 that is predicted for dark matter halos. There is a linear beta-j(*)/M-* relation for beta less than or similar to 0.4, exhibiting a general trend of increasing beta with decreasing j(*)/M-*. Galaxies with beta >= 0.4 have higher j(*) than predicted by the relation. Pseudobulge galaxies have preferentially lower beta for a given j(*)/M-* than galaxies that contain classical bulges. Pseudobulge galaxies follow a well-defined track in beta-j(*)/M-* space, consistent with Obreschkow & Glazebrook, while galaxies with classical bulges do not. These results are consistent with the hypothesis that while growth in either bulge type is linked to a decrease in j(*)/M-*, the mechanisms that build pseudobulges seem to be less efficient at increasing bulge mass per decrease in specific angular momentum than those that build classical bulges.