Not much space there to turn for a 'run' especially without tugs!!
Come up the Solent at full speed, keeping close in to the quayside (Starboard side). As you get a short distance away from the Dock, throw a mooring line out from about 2/3 of the way up. She'll swing into the dock at almost full speed if you get the right bollard at the right time. It's all in the wrist action.