The green hydrogen provides a pathway to the 100% sustainable energy future, rendering hydrogen energy service providers (HESPs) an important role in energy supply. Different from the conventional electricity service providers, HESP is not only responsible for the production, purchase and retailing but also the transportation of hydrogen, which makes its operation a challenging problem. To this end, this paper proposes a bi-level strategic operation model for HESPs. In the operation level, the bidding, hydrogen production and hydrogen transportation are coordinated to minimize the overall cost of HESPs. In the market level, the market clearing is simulated to estimate the influence of HESP behavior on electricity prices in the market. Then, a model reformulation technique is developed to connect the discrete-time based hydrogen production and continuous-time based hydrogen transportation. The bi-level optimization model is transformed into a single-level mixed-integer linear programming (MILP) problem with Karush-Kuhn-Tucker (KKT) conditions. The case studies with the modified IEEE-RTS-79 system were given to validate the proposed model and confirm the necessity to coordinate the hydrogen production and transportation in the strategic operation of HESPs. Sensitivity analysis is also conducted to study the potential influencing factors.