Berths and handling machinery are critical and scarce resources in bulk port operations. To improve the overall port operational efficiency, this paper addresses the continuous berth allocation and handling machinery assignment problem under dynamic vessel arrivals. Considering realistic factors such as the tidal constraint, berth preferences, and interference between handling machinery, a mixed-integer nonlinear programming model is presented for this problem to minimize the total costs of all vessels over the planning horizon, comprising waiting costs, berth deviation costs, delay costs, and handling machinery usage costs. The proposed model is linearized and subsequently solved using CPLEX. Numerical experiments conducted on randomly generated instances from a Chinese port, with multiple operational scales, validate the model. Sensitivity analyses on the deviation coefficient of berth handling efficiency and the handling machinery interference coefficient provide recommendations for port scheduling, offering insights for port operations practice.