  We provide two examples of smooth projective surfaces of tame CM type, by
showing that any parameter space of isomorphism classes of indecomposable ACM
bundles with fixed rank and determinant on a rational quartic scroll in
projective 5-space is either a single point or a projective line. For surfaces
of minimal degree and wild CM type, we classify rigid Ulrich bundles as
Fibonacci extensions. For the rational normal scrolls S(2,3) and S(3,3), a
complete classification of rigid ACM bundles is given in terms of the action of
the braid group in three strands.
