  We consider the following question: for which invariants $g$ and $e$ is there
a geometrically ruled surface $S \rightarrow C$ over a curve $C$ of genus $g$
with invariant $e$ such that $S$ is the support of an Ulrich line bundle with
respect to a very ample line bundle? A surprising relation between the
existence of certain proper Theta divisors on some moduli spaces of vector
bundles on $C$ with the existence of Ulrich line bundles on $S$ will be the key
to completely solve the above question. The relation is realized by translating
the vanishing conditions characterizing Ulrich line bundles to specific
geometric conditions on the symmetric powers of the defining vector bundle of a
given ruled surface. This general principle leads to some finer existence
results of Ulrich line bundles in particular cases. Another focus is on the
rank two case where, with very few exceptions, we show the existence of large
families of special Ulrich bundles on arbitrary polarized ruled surfaces.
