With the rapid growth of intermittent renewable energy sources, it is critical to ensure that renewable power generators have the capability to perform primary frequency response (PFR). This paper proposes a framework for using a shared battery energy storage system (BESS) to undertake the PFR obligations for multiple wind and photovoltaic (PV) power plants and provide commercial automatic generation control (AGC) service in the ancillary service market at the same time. Furthermore, an optimal bidding strategy in the hour-ahead energy and ancillary service markets is proposed to maximize the BESS' benefits, considering frequency regulation performance, battery degradation cost, and the state of charge (SoC) limits. The optimization model is first built as a chance-constrained optimization problem and then transformed into mixed-integer quadratically constrained programming using Wasserstein metric-based distributionally robust optimization technique. Simulation results show that the proposed optimal bidding strategy and solution method can effectively take advantage of a BESS to perform PFR and provide AGC services simultaneously and improve its economic benefits.