Sarashi
Japanese Living

The bancho is a type that regularly appeared in manga and TV animation in the Sixties and early Seventies. Bancho is in the dictionary as "juvenile gang leader." Sarashi is a long strip of white cotton cloth, wrapped around the midriff. It used to be worn by samurai under their kimono, to make it harder to be wounded in sword fights. Because this is so tough, yakuza and young ruffians wore sarashi until fairly recently as a sign of their badness.

Relevance to Urusei Yatsura

With this in mind Ryunosuke wearing a sarashi holds a double meaning. Practically speaking since her father won't let her get a bra, it's for support. The side effect being that it covers up her breasts so that when she wears clothing, she appears more like a boy. The more symbolic meaning behind it is that Ryunosuke being a rough n' tumble rebel who gets into a lot of fights, wearing a sarashi is in keeping with her character even if she was a boy. It's also been noted that Tobimaro wears a sarashi too, but in his case it's because of his bushido lifestyle.