  We prove that a continuous potential $q$ can be constructively determined
from the knowledge of the Dirichlet-to-Neumann map for the perturbed biharmonic
operator $\Delta_g^2+q$ on a conformally transversally anisotropic Riemannian
manifold of dimension $\ge 3$ with boundary, assuming that the geodesic ray
transform on the transversal manifold is constructively invertible. This is a
constructive counterpart of the uniqueness result of [51]. In particular, our
result is applicable and new in the case of smooth bounded domains in the
$3$-dimensional Euclidean space as well as in the case of $3$-dimensional
admissible manifolds.
