I looked into the Xiamen BRT more closely, and discovered the situation to be confusing indeed. It appears that the BRT line actually does not reach the airport. It is reachable only by an extension bus line L19, which has stops at both Terminal 3 and 4, and connects with the BRT station called Xianhou (县后). With that in consideration, it looks like BRT is NOT the way to go.

What I thought was BRT is actually Airport Express Bus, which run on regular roads. There several lines from T3 and T4, including one that goes nonstop to Xiamen Railway Station. From there, you can take either transfer to a regular city bus to Bailuzhou Park, or hail a taxi.

I also discovered that a regular city bus, line #27 , goes from T3 (but not T4) directly to Bailuzhou Park, albeit with many intermediate stops.