From Jinjiang Inn Huaihai Road (E), is there a bus route going to shanghai airport?

May I know whether you refer to Pudong Airport? If so, I'm afraid there is no a direct bus leading to the airport. Suppose u don't mind traveling by subway, I suggest you walk from ur hotel to Dashijie metro station to take metro line 8 to People's Square, where transfer to line 2 to PVG directly.