  We obtain a simple two-sided inequality for the ratio
$\mathbf{L}_\nu(x)/\mathbf{L}_{\nu-1}(x)$ in terms of the ratio
$I_\nu(x)/I_{\nu-1}(x)$, where $\mathbf{L}_\nu(x)$ is the modified Struve
function of the first kind and $I_\nu(x)$ is the modified Bessel function of
the first kind. This result allows one to use the extensive literature on
bounds for $I_\nu(x)/I_{\nu-1}(x)$ to immediately deduce bounds for
$\mathbf{L}_\nu(x)/\mathbf{L}_{\nu-1}(x)$. We note some consequences and obtain
further bounds for $\mathbf{L}_\nu(x)/\mathbf{L}_{\nu-1}(x)$ by adapting
techniques used to bound the ratio $I_\nu(x)/I_{\nu-1}(x)$. We apply these
results to obtain new bounds for the condition numbers
$x\mathbf{L}_\nu'(x)/\mathbf{L}_\nu(x)$, the ratio
$\mathbf{L}_\nu(x)/\mathbf{L}_\nu(y)$ and the modified Struve function
$\mathbf{L}_\nu(x)$ itself. Amongst other results, we obtain two-sided
inequalities for $x\mathbf{L}_\nu'(x)/\mathbf{L}_\nu(x)$ and
$\mathbf{L}_\nu(x)/\mathbf{L}_\nu(y)$ that are given in terms of
$xI_\nu'(x)/I_\nu(x)$ and $I_\nu(x)/I_\nu(y)$, respectively, which again allows
one to exploit the substantial literature on bounds for these quantities. The
results obtained in this paper complement and improve existing bounds in the
literature.
