This study proposes a two-step algorithm for demand forecasting of bento menus. The first step of algorithm involves quantifying the popularity of a product using a Bayesian estimation-based rating system. In the second step, demand forecasting is performed using machine learning that considers the quantified popularity of products from the first step. Daily sales forecasting is a constant challenge for bento delivery service companies. Many companies offer both bento menus, in which the same products are sold cyclically, and bento menus, in which a different product is sold each day. In many cases, forecasters perform predictions manually based on their experience. Demand forecasting with high accuracy is not easy because it is difficult to quantify the popularity of bento menu products. To demonstrate the usefulness of the proposed algorithm, numerical experiments were conducted using actual data provided by a bento delivery service company. The forecasting by the proposed algorithm was more accurate than that by the previous model. In addition, the proposed algorithm exhibited higher accuracy than the forecaster's predictions for several evaluation indicators.