Can I catch a bus from Beijing Airport to Tianjin cruise port (Sapphire Princess)?

No direct bus is available. Then I suggest you take a direct intercity bus from the airport to Tianjin Tianhuan Bus Station first. Upon getting there, you can take a taxi to the cruise terminal directly. Or walk to TJ Hospital for Infectious Diseases bus stop to take bus no. 835 to Tanghu Railway Station. There you can transfer to bus no. 102 to get there or catch a taxi to reach directly!