Galaxies exhibit coherent alignments with local structure in the Universe. This effect, called Intrinsic Alignments (IA), is an important contributor to the systematic uncertainties for wide-field weak lensing surveys. On cosmological distance scales, intrinsic shape alignments have been observed in red galaxies, which are usually bulge-dominated; while blue galaxies, which are mostly disc-dominated, exhibit shape alignments consistent with a null detection. However, disc-dominated galaxies typically consist of two prominent structures: disc and bulge. Since the bulge component has similar properties as elliptical galaxies and is thought to have formed in a similar fashion, naturally one could ask whether the bulge components exhibit similar alignments as ellipticals? In this paper, we investigate how different components of galaxies exhibit IA in the TNG100-1 cosmological hydrodynamical simulation, as well as the dependence of IA on the fraction of stars in rotation-dominated structures at z = 0. The measurements were controlled for mass differences between the samples. We find that the bulges exhibit significantly higher IA signals, with a nonlinear alignment model amplitude of $A_I = 2.98^{+0.36}_{-0.37}$ compared to the amplitude for the galaxies as a whole (both components), $A_I = 1.13^{+0.37}_{-0.35}$. The results for bulges are statistically consistent with those for elliptical galaxies, which have $A_I = 3.47^{+0.57}_{-0.57}$. These results highlight the importance of studying galaxy dynamics in order to understand galaxy alignments and their cosmological implications.