Energy markets must match the real-time power supply and demand; however, the increasing penetration of stochastic renewables into the power grid is causing uncertainties in the capability of the power system to eliminate this power mismatch. The ability to store electrical energy in a battery energy storage system can improve the frequency control of the power grid, making it more reliable and efficient. However, with such heavy investments in the battery storage system, the storage provider must be able to gain significant profit-earning opportunities. This paper proposes a novel multi-stage stochastic bidding strategy for the grid-level battery storage system to maximize the arbitrage under the day-ahead (DA) and the real-time (RT) forecasted market price uncertainty in co-optimized energy, regulation and flexible ramping product (FRP). The proposed bidding strategy is used in the co-optimized DA and RT market framework and tested through case studies in the context of the Australian Electricity Market. The paper demonstrates that the proposed strategy can increase the overall arbitrage, the frequency control of the grid and the profit for the storage provider even under price uncertainty.