The spin excitations in a bond-centered stripe phase, where strong dimerization coexists with weak collinear magnetic order, were studied. It was observed that the transverse modes resemble semiclassical spin waves at low energies, but cross over into triplet modes of dimerized ladders at higher energies. It was suggested that the spin ordering in La compound is far from the semiclassical limit, and strong quantum effects related to dimerization dominate the spectrum at high energies. For small doping , semiclassical spin-wave approach was expected to be more appropriate for the whole energy range.