With the growing penetration of renewable energy resource, electricity market prices have exhibited greater volatility. Therefore, it is important for Energy Storage Systems(ESSs) to leverage the multidimensional nature of energy market bids to maximize profitability. However, current learning methods cannot fully utilize the high-dimensional price-quantity bids in the energy markets. To address this challenge, we modify the common reinforcement learning(RL) process by proposing a new bid representation method called Neural Network Embedded Bids (NNEBs). NNEBs refer to market bids that are represented by monotonic neural networks with discrete outputs. To achieve effective learning of NNEBs, we first learn a neural network as a strategic mapping from the market price to ESS power output with RL. Then, we re-train the network with two training modifications to make the network output monotonic and discrete. Finally, the neural network is equivalently converted into a high-dimensional bid for bidding. We conducted experiments over real-world market datasets. Our studies show that the proposed method achieves 18% higher profit than the baseline and up to 78% profit of the optimal market bidder.