  We present a $(1+\frac{k}{k+2})$-approximation algorithm for the Maximum
$k$-dependent Set problem on bipartite graphs for any $k\ge1$. For a graph with
$n$ vertices and $m$ edges, the algorithm runs in $O(k m \sqrt{n})$ time and
improves upon the previously best-known approximation ratio of
$1+\frac{k}{k+1}$ established by Kumar et al. [Theoretical Computer Science,
526: 90--96 (2014)]. Our proof also indicates that the algorithm retains its
approximation ratio when applied to the (more general) class of
K\"{o}nig-Egerv\'{a}ry graphs.
