the Jinan Airport and the Taishan Shuttle Terminal

Well, there is no Taishan Shuttle Terminal. It's Taian Terminal, which is not far from Mt. Taishan. The distance is about 71 miles.
According to your arrival time, there is no bus for you to take. So it's suggested to find a hotel nearby and start off in the next early morning.
The bus schedules are 10:30, 12:00, 13:30, 15:00, 16:30, 18:00, 19:30 and 21:00. It takes around 1.5 hours on the way. Then take a taxi to the scenic area directly.