is there a public bus from Xian great goose pagoda to terra cotta warriors? where? what number?

Yes, but there is a direct bus! You are advised to take bus no. 5, 500 or 30 at the South Square of the Big Wild Goose Pagoda (Dayantan Nanguangchang) stop to XA Railway Station. Then at the east square of the train station, you can take Tourism bus line 5 (no. 306), no. 914 or 915 to the Terracotta Warriors directly!