What is available?
Alan, go to Berlinlinienbus.de (www.) click on the little British flag on the top right for the English version. It looks like they have several departures a day - 19 Euro one way being the cheapest ticket. Seems the trip takes three hours and 10 minutes. Sounds like a terrific deal and takes you right downtown.
With a Dauer-Spezial fare (adv purchase, non-refundable) you can go from downtown Hamburg to downtown Berlin via InterCityExpress (ICE, yeah, that's a train) in 1hr 39min for as low as €29.