The paper addresses robust bilevel optimization with polyhedral uncertainty in the followers’ objective function coefficients. It is assumed that both the leader’s and the followers’ models are linear, yet, bilinear terms in the followers’ objective function are allowed. An efficient algorithm is introduced that finds a bounded-error solution in a finite number of steps. This model captures typical price setting applications, such as network toll setting or electricity tariff optimization for demand response management. The efficiency of the general method is illustrated on demand response management in smart grids. Our computational experiments show that the method solves instances with hundreds of decision variables. The significance of these results is underlined by a proof that the above demand response management problem, and hence, the generic robust bilevel problem as well, are sum 2-p complete. Finally, the infinitely robust variant of the problem is discussed, and it is shown to be tractable in polynomial time.