Information on congestion of buses, which are one of the major public transportation modes, can be very useful in light of the current COVID-19 pandemic. Because it is unrealistic to manually monitor the number of riders on all buses in operation, a system that can automatically monitor congestion is necessary. The main goal of this paper's work is to automatically estimate the congestion level on a bus route with acceptable performance. For practical operation, it is necessary to design a system that does not infringe on the privacy of passengers and ensures the safety of passengers and the installation sites. In this paper, we propose a congestion estimation system that protects passengers' privacy and reduces the installation cost by using Bluetooth low-energy (BLE) signals as sensing data. The proposed system consists of (1) a sensing mechanism that acquires BLE signals emitted from passengers' mobile terminals in the bus and (2) a mechanism that estimates the degree of congestion in the bus from the data obtained by the sensing mechanism. To evaluate the effectiveness of the proposed system, we conducted a data collection experiment on an actual bus route in cooperation with Nara Kotsu Co., Ltd. The results showed that the proposed system could estimate the number of passengers with a mean absolute error of 2.49 passengers (error rate of 38.8%).