Data centers can adjust their load through computing task scheduling, which will become an important flexible demand-side regulation resource in new power systems. However, data centers and power systems have different operation objectives and cannot fully share information. An effective bidirectional coordination method for computing power and electric power has not yet been established. This paper proposes a bidirectional collaborative optimization method for computing power and electric power driven by computing task scheduling from a cooperative game perspective. First, a bidirectional coordinative optimization framework for data center operators and power system operators is proposed based on the Nash bargaining theory, to coordinate utility improvements for both parties. Next, detailed computing task scheduling models for interactive workloads and batch jobs are established, and a computing task scheduling decision-making method based on rolling horizon optimization is proposed. Subsequently, a distributed online solution method for collaborative decision-making of computing power and electric power is proposed. It balances global optimality and real-time solution efficiency while preserving the confidentiality of internal operation parameters and information of both parties. Case study results verify the effectiveness of the proposed method.