You can go to the Sulphur springs and drive in volcano by taxi. There are taxis on the outside from where you will be docking so that makes it easier for you. If you would like me to recommend someone to you that will give you a reasonable rate, I can do so for you.
There are also special tours that allow you to travel by sea then take a taxi from the Soufriere docking area to the sulphur springs.
Those are your two options for getting to the sulphur springs.