Since the Tokugawa period was marked by general policy of isolationism, I am having trouble understanding who would know both English and Japanese and be able to do the translating.
User /u/diana_mn in their comment here details the exact people who were used as translators during the mission as well as the languages they spoke.
EDIT: That same user also answered many followup questions to the same answer in this thread that add significant amounts of context that you may find interesting.