We study optimistic robust bilevel problems with uncertainty in the follower’s problem, where the follower adopts a so-called wait-and-see approach. In this setting, the leader decides without knowledge of the specific realization of the uncertainty. Then, the uncertainty realizes in a worst-case manner, and afterward the follower makes her own decisions. For this challenging problem class, we present a general solution approach based on column-and-constraint generation (CCG), which iteratively solves a bilevel master problem involving a single leader and multiple followers, along with (pessimistic) bilevel subproblems. We analyze structural properties of this problem class, including solution attainability, and show that worst-case realizations of the uncertainty need not occur at extreme points of the uncertainty set. Building on these insights, we establish finite termination and exactness for discrete uncertainty or finitely many upper-level decisions. Moreover, for polyhedral uncertainty sets, we prove that a solution of arbitrary precision can be computed in finitely many iterations. Finally, we demonstrate the applicability of the presented approach through an extensive computational study on two application domains, including both continuous and integer lower-level decisions.