Improving the positioning accuracy and stability of a single BDS/INS sensor system in agricultural machinery is important for expanding the application scenarios of agricultural machinery. This paper proposes a navigation and positioning model based on an improved bee-colony-algorithm-optimized BP network (the IABC-BP model). The main aspect of this work involves introducing adaptive coefficients and speed adjustment coefficients that obey Gaussian distribution to ensure the balance between the rate of convergence, group flexibility, and searchability in the search process. The implicit adaptive layer formula of the BP network is proposed, and the BDS/INS navigation and positioning model for agricultural machinery is established using the IABC algorithm and the Kalman filter. Simulation tests and analyses of real-world application scenarios were conducted on the model, and the results showed that, compared with the original model, the performance of the model improved by 90.65%, 84.11%, and 25.96%, indicating that the proposed model has high accuracy and effectiveness. In the information fusion and compensation correction mode, the algorithm processes errors such as longitude and latitude within the target range and can achieve reliable navigation and positioning accuracy in a short period. At the same time, the model has good stability and generalization ability, and can be applied to other navigation scenarios in the future to expand its application scope.