  We compute bulk properties of Heisenberg spin-1/2 ladders using
Rayleigh-Schr\"odinger perturbation theory in the rung and plaquette bases. We
formulate a method to extract high-order perturbative coefficients in the bulk
limit from solutions for relatively small finite clusters. For example, a
perturbative calculation for an isotropic $2\times 12$ ladder yields an
eleventh-order estimate of the ground-state energy per site that is within
0.02% of the density-matrix-renormalization-group (DMRG) value. Moreover, the
method also enables a reliable estimate of the radius of convergence of the
perturbative expansion. We find that for the rung basis the radius of
convergence is $\lambda_c\simeq 0.8$, with $\lambda$ defining the ratio between
the coupling along the chain relative to the coupling across the chain. In
contrast, for the plaquette basis we estimate a radius of convergence of
$\lambda_c\simeq 1.25$. Thus, we conclude that the plaquette basis offers the
only currently available perturbative approach which can provide a reliable
treatment of the physically interesting case of isotropic $(\lambda=1)$ spin
ladders. We illustrate our methods by computing perturbative coefficients for
the ground-state energy per site, the gap, and the one-magnon dispersion
relation.
