This is not easily, generally answerable however. Prices in Japan vary heavily depending where you are. Renting a car in Okinawa, Osaka and downtown Tokyo will have quite different prices, same goes for motorbikes.
On top of that, as you probably know, bikes vary in spec massively. Since you do not indicate if you want to rent a 50cc or a custom-built Harley, a price will be even harder to determine.
I also want to point out that unless you speak Japanese well enough to discuss contract terms, you might have issues with some companies to get a contract signed. On top of that, some smaller Japanese companies might not rent to foreigners, no matter how well you speak Japanese. They will want to have a Japanese phone number and/or address.
If you know someone in Japan who can assist you (maybe even your hotel in Osaka can do that) to find a company that will give you a bike, this will of course be very helpful.
So planning will be crucial in this. There are several companies renting out bikes obviously. If you want to Google yourself, the term is "rentalbike", in Japanese "レンタルバイク" and Osaka is written "大阪"
Googling that, the first company on the results for example rents out a variety from 50cc to 1200cc, starting with 4'000 Yen a week for the smallest and topping out at 25'000 Yen for a week. I guess you will have to pick your preferred model.