In this work, a real-time subsidy based robust scheduling method for the integrated gas and power system is proposed. Bi-directional energy conversion, including the power-to-gas and gas-fired generation, is operated via dynamic variant price signals. The gaming between the electrical power system and the natural gas system is formulated in the bi-level optimization. The upper-level problem minimizes the operational cost, in which the real-time subsidy for power-to-gas and gas-fired units is obtained. The lower-level problem maximizes the profit for the power-to-gas and gas-fired units, in which the transient gas flow is introduced. In addition, in order to counter the uncertainties brought on by wind power, a real-time subsidy update strategy based on robust optimization is proposed to stimulate the regulation capabilities of the power-to-gas and gas-fired units. This bilevel optimization is reformulated as a mixed-integer quadratic programming problem using the Karush-Kuhn-Tucker optimization conditions. Simulation results show that the real-time subsidy scheduling can make power to-gas and gas-fired units follow the system operator's preferences such as wind power accommodation, mitigation of unsupplied load, and relieving network congestion.