Well, I would say suck it up and finish your degree here. It's just plain worth it to do so. Also, I don't really think many of the scholarships out there for one-year exchanges will take you as a grantee if you've already done an exchange to Japan.
There is, however, Temple University's Tokyo campus-- you could try applying to transfer there (they can take you if you've finished a couple years of college) and finish off your degree there. They do offer some scholarships as well, so I guess you can at least check it out.
After you've finished your bachelor's there is the monbukagakusho scholarship for postgrad. A number of folks who visit this forum (myself included) are on board for that this year. If you don't know much about it, initially you can have up to two years as a postgrad research (non-degree) student, with the option of extending to get a degree (master's or even PhD) if you pass your school's entrance exam.
You have to have a good clear idea of what you actually want to do academically, and write up a strong proposal. It also helps to find a professor who is willing to take you as a student, or better yet, interested in having you there. If you are a good student and have a good plan, you have a reasonable shot at getting this scholarship.
Do that, and your master's is funded, piece of cake. There's almost no other way to do that, as far as I know, except to *have* the money.
There is also the JET program. I would really only encourage you to do that if you're interested in being an ALT and eventually moving on to be a full teacher, but I guess a lot of people do it for the experience or to live in Japan for a while, so nothing wrong with that. I do encourage you to have an idea of what you want to do long term, though. Being in Japan for the sake of being there isn't really a career.
I'm not saying not to take a couple of years and do something that isn't a long term thing, that's fine.. but it's good to have at least some practicalities in mind.