Reforming of methane with carbon dioxide has been carried out using a bipolar pulse driven elongated arc reactor operating at atmospheric pressure and non-equilibrium regime. This plasma reactor is driven by two kinds of power supply, characterized by different voltage-current characteristics under the same operating power and frequency. Varying the $CO_2/CH_4$ ratio and the discharge power, the conversion rate, yield, and reforming efficiency for the two power supplies are investigated in conjunction with the static and dynamic behaviors of voltage and current. It is found that not only the values of voltage and current but also their shapes give an influence on the reforming performances. Finally, a better electrical operation regime for the efficient plasma reforming is proposed based on the relationship between the voltage-current characteristics and the reforming performance.