Bourbon virus (BRBV) was first isolated from a patient hospitalized at the University of Kansas Hospital in 2014. Since then, several deaths have been reported to be caused by BRBV infection in the Midwest and Southern United States. BRBV is a tick-borne virus that is widely carried by lone star ticks. It belongs to genus Thogotovirus of the Orthomyxoviridae family. Currently, there are no treatments or vaccines available for BRBV or thogotovirus infection caused diseases. In this study, we reconstituted a replicon reporter system, composed of plasmids expressing the RNA-dependent RNA polymerase (RdRP) complex (PA, PB1, and PB2), nucleocapsid (NP) protein, and a reporter gene flanked by the 3' and 5' untranslated region (UTR) of the envelope glycoprotein (GP) genome segment. By using the luciferase reporter, we screened a few small molecule compounds of anti-endonuclease that inhibited the nicking activity by parvovirus B19 (B19V) NS1, as well as FDA-approved drugs targeting the RdRP of influenza virus. Our results demonstrated that myricetin, an anti-B19V NS1 nicking inhibitor, efficiently inhibited the RdRP activity of BRBV and virus replication. The IC50 and EC50 of myricetin are 2.22 and 4.6 μM, respectively, in cells. Myricetin had minimal cytotoxicity in cells, and therefore the therapeutic index of the compound is high. In conclusion, the BRBV replicon system is a useful tool to study viral RNA replication and to develop antivirals, and myricetin may hold promise in treatment of BRBV infected patients.