Network design problems increasingly arise in settings where strategic infrastructure decisions and operational routing choices are made by different actors. Such interactions are naturally modeled as bilevel problems: a network operator designs or modifies a network, while users respond by selecting routes according to their own utilities. This structure captures many applications in transportation and mobility planning, yet exact solution methods remain difficult to apply, and many real-world bilevel network design applications are still addressed primarily by heuristics. In this paper, we aim to bridge this gap by studying three major exact MIP formulations: the Strong Duality Reformulation (SDR), the Benders-like Decomposition (BlD), and the Path-Based Reformulation (PBR). We compare the strength of their LP bounds and introduce a hybrid reformulation that combines their complementary strengths. We then focus on instances in which existing network infrastructure is expanded or modified, for which we introduce preprocessing techniques based on bilevel feasible paths that strengthen all discussed reformulations. Computational experiments on instances motivated by real-world transit network design applications show that the proposed preprocessing techniques lead to order-of-magnitude performance improvements over the standard reformulations considered in this paper. All methods are implemented in the open-source Julia package JuBiC, enabling practitioners to apply the discussed techniques to their own bilevel network design applications