We study optimal bidding strategies for advertisers in budget constrained multi-item multi-slot auctions. The classic application context is that of bidding in sponsored search auctions. In general, these auctions are run as variants of second-price auctions but have been shown to be incentive incompatible. Thus advertisers have to be strategic about bidding. Uncertainty in the decision-making environment, budget constraints and the presence of a large portfolio of candidate keywords makes the optimization problem non-trivial. We first present an analytical model to characterize the optimal bidding strategy and illustrate its application using real-world data. We find that the proposed strategies are very effective in practice.