Embedding bivariate probability density functions in Bayes spaces enables their orthogonal decomposition into independent and interactive parts, the former can be further decomposed into orthogonal geometric marginals. After performing the clr (centered logratio) transformation, densities can be analysed as functional data in 𝐿20 space. In this paper, we focus on functional principal component analysis(FPCA) and its use for bivariate densities as well as for the vector of orthogonal densities from their decomposition. We show that performing FPCA on the original bivariate densities is equivalent to performing multivariate FPCAon the decomposed densities (the vector of the interactive part and geometric marginals). Moreover, eigenfunctions and scores decompose accordingly, and this allows to identify which parts of the decomposition contribute the most to the variation of the densities. The theoretical results are complemented by an illustration on an empirical data set.