The Rocket runs from Barisal’s Rocket Ghat to either Dhaka, in one direction, or Morrelganj in the other. It used to run all the way to Khulna, but silting of the riverbed has made the river too shallow for the vessel to travel beyond Morrelganj.
If you want to go as far as Khulna, you can catch the Rocket up to Hularhat, then take a bus to Khulna from there. Note, the Rocket to Dhaka stops for half an hour in the small fishing town of Chandpur (Tk 650, seven hours), from where you can get to Chittagong by bus. For daytime Rocket trips, just buy your ticket on board, half an hour before departure. For overnight trips to Dhaka, you must reserve your ticket at the BITWC office, on the 2nd floor of an unmarked building across the main road from the ferry ghat.