As the cost of battery energy storage continues to decline, we are likely to see the emergence of merchant energy storage operators. These entities will seek to maximize their operating profits through strategic bidding in the day-ahead electricity market. One important parameter in any storage bidding strategy is the state-of-charge at the end of the trading day. Because this final state-of-charge is the initial state-of-charge for the next trading day, it has a strong impact on the profitability of storage for this next day. This paper proposes a look-ahead technique to optimize a merchant energy storage operator’s bidding strategy considering both the day-ahead and the following day. Taking into account the discounted profit opportunities that could be achieved during the following day allows us to optimize the state-of-charge at the end of the first day. We formulate this problem as a bilevel optimization. The lower-level problem clears a ramp-constrained multiperiod market and passes the results to the upper-level problem that optimizes the storage bids. Linearization techniques and Karush-Kuhn-Tucker conditions are used to transform the original problem into an equivalent single-level mixed-integer linear program. Numerical results obtained with the IEEE Reliability Test System demonstrate the benefits of the proposed look-ahead bidding strategy and the importance of considering ramping and network constraints.