Since when do community colleges offer bachelor's degrees? I don't think they do. You're going to have to finish a 4-year program (2 at community college, 2 elsewhere) or study through the summer and finish at an accelerated pace somehow, but you will still need to get the BA at another place.
You can apply to JET programme or conversation schools before you graduate, but not long before! They need some assurance that you truly will get that BA degree, mostly because the work visa hinges on it.
Get the degree. Apply. Hope for the best. You can come here and apply but realize a few things.
1) JET accepts applications from within Japan, but their once-a-year process is limited to interviewing people in their home countries, not Japan.
2) Reiterating, JET interviews only once a year.
3) Come here, and you have more opportunities to find work than if you were to stay home, but you will have to support yourself. Probably for 2-4 months. That means having US$4000-5000 in your pocket before you see a first paycheck.
4) Stay home and apply, and you have fewer opportunities, but at least you won't have to fork out that money.
5) The places that interview abroad don't go everywhere for interviews, though, and you will be expected to pay for the time spent getting there (whether it's Chicago, San Francisco, or Toronto), and some of those interviews last 1-3 days. Some places interview all year round, while others have designated timetables.