Persistence diagram (PD) bundles, a generalization of vineyards, were recently introduced as a way of studying the persistent homology of a set of filtrations parameterized by a topological space $\mathcal{T}$. In this paper, I present an algorithm for computing piecewise-linear PD bundles, a wide class that includes many of the PD bundles that one may encounter in practice. I give full implementation details for the case in which $\dim(\mathcal{T}) \leq 2$, and I outline the generalization to higher dimensions.