I commute by bicycle. I don't like carrying bags on me because they trap sweat underneath them (which is especially bothersome in Japan's humid climate). The front basket on my bicycle is large enough to carry a backpack, but I've found that it's not big enough to carry all the things that I normally bring with me to work and my Naginata gi (uniform).
Also at some point I'm probably going to be bringing bogu (armor) with me. Unfortunately I can't just keep it in the dojo like most people do because I'd probably be using it regularly in two different places. So I bought this rear basket. It expands to be bigger, and it's the biggest basket I could find online. I'm pretty sure bogu will fit into it. It's also convenient because it has handles like a shopping basket and can detach from the rear rack with the push of a button. It'll be really easy to carry things around!