  We define notions of semi-saturatedness and orthogonality for a Fell bundle
over a quasi-lattice ordered group. We show that a compactly aligned product
system of Hilbert bimodules can be naturally extended to a semi-saturated and
orthogonal Fell bundle whenever it is simplifiable. Conversely, a
semi-saturated and orthogonal Fell bundle is completely determined by the
positive fibres and its cross sectional $\mathrm{C}^*$-algebra is isomorphic to
a relative Cuntz--Pimsner algebra of a simplifiable product system of Hilbert
bimodules. We show that this correspondence is part of an equivalence between
bicategories and use this to generalise several results of Meyer and the author
in the context of single correspondences. We apply functoriality for relative
Cuntz--Pimsner algebras to study Morita equivalence between
$\mathrm{C}^*$-algebras attached to compactly aligned product systems over
Morita equivalent $\mathrm{C}^*$-algebras.
