Is there a direct bus service from Fuzhou Airport to Jinjiang? If available, when is the last bus?

No, there is no direct long-distance between these two places. Thus you are suggested to take shuttle bus to the South Railway Station first. The duration is about an hour. And the ticket fare is CNY 25 per person.
After arriving, there are several high-speed trains that can take you to Jinjiang. The train schedules are 07:20, 07:57, 08:13, 17:19, 17:29 and 21:18. It takes around 1.5 hours. And the ticket fare of second class seat is CNY52.5 and first class seat is CNY63.5.