It's not Japanese media but Leliana from Dragon Age is bi and she's a very respectable character. Zevran is also bi but he's thoroughly amoral. Also those particular elements of their character do not consume their character. Zevran is a slut so sex does come up a lot with him, but Leliana doesn't wear her sexuality on her sleeve. I think you may approve of the way they handled her.
You know, the main reason I got DA:O was because I kept hearing about an awesome gay character that was in it. Little did I know that he was bisexual and that he was just a horndog. In Leliana's case, I wholeheartedly agree with you. I thought her entire character was well done and I really respected how her character wasn't only based around her sexuality, but also her past.
On the flipside, I didn't like the way they handled Zevran's sexuality. To me, it had the same problem as with Kanji's in P4 in that they don't really handle the male attraction aspect of their character well. In Kanji's case, it felt like they just added that part of his character in order for the other characters to make fun over it in the course of the game. With Zevran, they made him very sexually outgoing (for lack of a better word) towards female characters, but you actually had to talk to him for quite a bit before he started getting that way towards male characters. Also, the only important relationships that actually affected Zevran in his past were all female, but all the male relationships he had were all just rendered into jokes. I'm not saying he was a bad character (because he wasn't), but he wasn't a very good character to properly show a gay character or even a bisexual character with more preference towards males.
It's like he said, with his kind of past, he takes whatever pleasures he can find which makes me think that he's not necessarily bi, but rather, doesn't mind having sexual relationships with males.