So, what to do? If, as you say, you're on a bicycle, why not just get a set of waterproof panniers? Ortlieb makes several: the Front-Roller panniers are only $120 (U.S.) for a pair, and they're totally waterproof (www.ortlieb.com). Carrying capacity per pair is around 25 liters, which sounds like it could fit your needs. They also clip right off a luggage rack, while a handy shoulder strap makes it easy to haul them around. Ortlieb even makes a clip-on strap system that converts any pannier to a backpack (the straps are about $40). A Nagoya-based company called PR International distributes Ortlieb gear in Japan, so you might want to drop them an e-mail or give them a call (www.g-style.ne.jp).
Alternatively, wear a regular pack and waterproof the contents. Several companies make waterproof inserts that simply go inside the packeven if the pack is soaked, the stuff inside the insert stays dry. Exped makes one called the Waterproof Pack Liner (www.exped.com). The small model, with a capacity of 40 liters, is only $20, which I imagine would work just fine for your books, various teaching tools, and bento box!