Is there a bus that runs from Tianjin Airport to Beijing Capital Airport and how often do they leave?

Hi Andrew, there is no direct bus from Tianjin Airport to Beijing Capital Airport。 The best way from Tianjin Airport to Beijing Airport is as follows:
Take Tianjin Airport Shuttle Bus (天津机场客运区－南京路（香槟小镇）) and then take taxi to Tianhuan Bus Station(天环客运站), after arriving, take direct bus to Beijing Capital Airport, the timetable of buses from Tianhuan Bus Station to Beijing Capital Airport is from 04:00 in the morning to 18:00 in the evening with one hour interval, the last bus leaves at 18:30.