How do we get to Huangyaguan Pass by bus? We are staying at Tianjin First Hotel in Nth Jiefang Road

You need to get to Jixian County first:
By long-distance bus: From your hotel, walk to Xiaoyingmen to take bus 641 to Jianchang Road, then walk to Hebei Long-distance Bus Station. From there, take a long-distance bus to Jixian County; remember to take those going via express road, by which the duration is about 1.5-2 hours. Upon arrival, I recommend you take a minibus to the site directly rather than by changing city buses for several times. The minibus fare is about CNY 100 for a single trip; you can share one with others to save money.

By train: From your hotel, walk to Qufu Road to take bus no. 196, 13 or 953 to Tianjin Railway Station (just two stops), then take a train to Jixian County. The train schedules are at 07:24 and 09:30. Duration is about 2-3 hours. Upon arrival, hire a minibus to the attraction site; the fare is not much difference than from the Jixian Coach Center.