We present the relation between stellar specific angular momentum j*, stellar mass M*, and bulge-to-total light ratio {beta} for The HI Nearby Galaxy Survey, the Calar Alto Legacy Integral Field Area Survey, and Romanowsky & Fall (2012ApJS..203...17R) data sets, exploring the existence of a fundamental plane between these parameters, as first suggested by Obreschkow & Glazebrook (2014ApJ...784...26O). 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}<~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.