We consider an electricity supplier for a large commercial electric vehicle (EV) fleet. The supplier uses a dynamic pricing scheme for buying and selling energy from and to the fleet, enabling the supplier to trade any deviations from the agreed day-ahead (DA) position in the intraday auction (IDA) market, while taking into account the behavior of the fleet and its participation in vehicle-to-grid (V2G) services. We propose a bilevel optimization model to capture the hierarchical interaction between the two agents. At the upper level, the supplier maximizes its profit, whereas at the lower level, the EV fleet owner minimizes its total energy cost under a predetermined trip schedule. Because the follower model includes complementarity constraints, we use McCormick envelope relaxation to linearize them, and we prove that the linear relaxation of the lower-level problem is equivalent to the original formulation. We reformulate the model into an equivalent single-level formulation and solve it using an off-the-shelf solver. The model is evaluated through a case study on the Iberian electricity market, comparing results with a baseline that follows the agreed DA position with no adjustments in the IDA market and no V2G. The results confirm that the proposed model improves the economic position of both supplier and fleet owner.