This work presents BIDS (Bidding using Diversified Search), an algorithm that can be used by negotiating agents to search very large outcome spaces. BIDS provides a balance between being rapid, accurate, diverse, and scalable search, allowing agents to search spaces with as many as 10 250 possible outcomes on very run-of-the-mill hardware. We show that our algorithm can be used to respond to the three most common search queries employed by 87% of all agents from the Automated Negotiating Agents Competition. Furthermore, we validate one of our techniques by integrating it into negotiation platform GeniusWeb, to enable existing state-of-the-art agents (and future agents) to scale their use to very large outcome spaces.