We will be going from the Intercity Hotel Berlin Hauptbahnhof near the Berlin Central train Station to Berlin Tegal Airport. Is there a shuttle that we can take for 4 passengers?
This service only takes 15 to 20 minutes.
http://www.vbb.de/en/index.html
Look on the site linked by Jazz for the TXL Express bus route from Hauptbahnhof to Tegel. If you want more private transport just pick up a taxi outside the station.
The InterCity Berlin Hbf does not provide shuttle service to Tegel. It's not like an American hotel where you can expect the Hilton or Marriott to offer shuttle service as is in LA or Orange Co.