This paper studies the synergy of solar-battery energy storage system (BESS) and develops a viable strategy for the BESS to unlock its economic potential by serving as a backup to reduce solar curtailments while also participating in the electricity market. We model the real-time bidding of the solar-battery system as two Markov decision processes for the solar farm and the BESS, respectively. We develop a novel deep reinforcement learning (DRL) algorithm to solve the problem by leveraging attention mechanism (AC) and multi-grained feature convolution to process DRL input for better bidding decisions. Simulation results demonstrate that our AC-DRL outperforms two optimization-based and one DRL-based benchmarks by generating 23%, 20%, and 11% higher revenue, as well as improving curtailment responses. The excess solar generation can effectively charge the BESS to bid in the market, significantly reducing solar curtailments by 76% and creating synergy for the solar-battery system to be more viable.