You need that bachelor's degree before any doors will open for you in Japan job-wise.But if you want to make the JET programme more or less a sure thing: pursue Japanese language studies, obtain tutoring or teaching experience (even on a volunteer basis), and travel internationally (or at least expand your world-view by familiarizing yourself with other cultures).
Passing the JET interview can be tough. Making sure you have the qualifications to impress the review board is important.
Consider completing TESL or TEFL courses by mail or at your university.
You have the time to prepare, be glad for it :)