  Let $G$ be a bipartite graph with bipartition $(X,Y)$. Inspired by a
hypergraph problem, we seek an upper bound on the number of disjoint paths
needed to cover all the vertices of $X$. We conjecture that a Hall-type
sufficient condition holds based on the maximum value of
$|S|-|\mathsf\Lambda(S)|$, where $S\subseteq X$ and $\mathsf\Lambda(S)$ is the
set of all vertices in $Y$ with at least two neighbors in $S$. This condition
is also a necessary one for a hereditary version of the problem, where we
delete vertices from $X$ and try to cover the remaining vertices by disjoint
paths. The conjecture holds when $G$ is a forest, has maximum degree $3$, or is
regular with high girth, and we prove those results in this paper.
