Grid-scale battery energy storage systems (BESSs) are promising to solve multiple problems for future power systems. Due to the limited lifespan and high cost of BESS, there is a cost-benefit trade-off between battery effort and operational performance. Thus, we develop a battery degradation model to accurately represent the battery degradation and related cost during battery operation and cycling. A linearization method is proposed to transform the developed battery degradation model into the mixed integer linear programming (MILP) optimization problems. The battery degradation model is incorporated with a hybrid deterministic/stochastic look-ahead rolling optimization model of wind-BESS bidding and operation in the real-time electricity market. Simulation results show that the developed battery degradation model is able to effectively help to extend the battery cycle life and make more profits for wind-BESS. Moreover, the proposed rolling look-ahead operational optimization strategy can utilize the updated wind power forecast, thereby also increase the wind-BESS profit.