  We investigate the influence of a cyclic spin exchange J_{cyc} on the one-
and two-triplet excitations of an undoped two-leg S=1/2 ladder, using the
density matrix renormalization group (DMRG). The dispersion of the S=0
two-triplet bound state is dramatically reduced by J_{cyc} due to a repulsion
between triplets on neighboring rungs. In (La,Ca)_{14}Cu_{24}O_{41} a
consistent description of both the spin gap and the S=0 bound state requires
$J_{cyc}/J_\perp \approx 0.20-0.27$ and $J/J_{\perp} \approx 1.25-1.35$. With
these coupling ratios the recently developed dynamical DMRG yields an excellent
description of the entire S=0 excitation spectrum observed in the optical
conductivity, including the continuum contribution.
