Modern neural encoders offer unprecedented text-image retrieval (TIR) accuracy, but their high computational cost impedes an adoption to large-scale image searches. To lower this cost, model cascades use an expensive encoder to refine the ranking of a cheap encoder. However, existing cascading algorithms focus on cross-encoders, which jointly process text-image pairs, but do not consider cascades of bi-encoders, which separately process texts and images. We introduce the small-world search scenario as a realistic setting where bi-encoder cascades can reduce costs. We then propose a cascading algorithm that leverages the small-world search scenario to reduce lifetime image encoding costs of a TIR system. Our experiments show cost reductions by up to 6x.