  We consider biconservative surfaces $\left(M^2,g\right)$ in a space form
$N^3(c)$, with mean curvature function $f$ satisfying $f>0$ and $\nabla f\neq
0$ at any point, and determine a certain Riemannian metric $g_r$ on $M$ such
that $\left(M^2,g_r\right)$ is a Ricci surface in $N^3(c)$. We also obtain an
intrinsic characterization of these biconservative surfaces.
