We were on Azamara Journey and disembarked there in 2014. I don't know of a shuttle bus, but there is regular bus service to and from the port. You catch it next to the terminal. We opted not to stay in Hamburg and rented a car from SIXT instead, which was at the terminal.
We were on the 70th Anniversary of WWII cruise which was awesome. Then when we disembarked, we tried to catch up to our church group that was doing a Reformation Tour as we neared the 500th anniversary of the Reformation. We rented a car from SIXT.