Don't look for a university study abroad program then.
There are many language schools that teach only Japanese. The students are still called 留学生, and they offer exchange-student visas, but they only teach Japanese.
The difficult thing with "business Japanese" is that you kinda need to know normal Japanese before you can learn business Japanese. I'm not exactly sure, but I think "Business English" is just a difficulty level that comes after "Advanced English".
I'm attending the YMCA College's language program right now. The YMCA was started in Japan in the 1800's some time, long before it became the fruity institution is in the States. The program I'm in is very good (although I have nothing to compare it to), and very rigorous (although only 6 hours a day, so less rigorous than Tony had it, I guess). The terms last 6 months, starting in April and October (you're probably too late to register for the next term).
There are other language schools that might fit your needs better, perhaps offering shorter programs or programs geared towards business people. Although my program does have a lot of older people in it (and is definately "adult level") most students are preparing for their first college career. I know it can be hard to find schools, and the worst part is that it's hard to know which school is good until you go to Japan and start visiting a few...