Virtual bidding plays an important role in two-settlement electric power markets, as it can reduce discrepancies between day-ahead and real-time markets. Renewable energy penetration increases volatility in electricity prices, making accurate forecasting critical for virtual bidders, reducing uncertainty and maximizing profits. This study presents a Transformer-based deep learning model to forecast the price spread between real-time and day-ahead electricity prices in the ERCOT (Electric Reliability Council of Texas) market. The proposed model leverages various time-series features, including load forecasts, solar and wind generation forecasts, and temporal attributes. The model is trained under realistic constraints and validated using a walk-forward approach by updating the model every week. Based on the price spread prediction results, several trading strategies are proposed and the most effective strategy for maximizing cumulative profit under realistic market conditions is identified through backtesting. The results show that the strategy of trading only at the peak hour with a precision score of over 50% produces nearly consistent profit over the test period. The proposed method underscores the importance of an accurate electricity price forecasting model and introduces a new method of evaluating the price forecast model from a virtual bidder's perspective, providing valuable insights for future research.