I don't see how that could be offensive to real bisexuals at all. In my experience, it can be real Truth in Television
. I'm a bisexual and I'm like that; I never really bring up my 'alternate' sexuality unless the situation specifically calls for it, but I have no problem expressing my interest in both sexes when having related conversations.
Though, it is true for me at least, that sometimes it can also be tiring to see 'bisexuals' who are so mostly just for some kind or gimmick or interest value, but in all their major relationships within the story they're in a heterosexual pair anyway. Sometimes when done this way, it can seem like a tacked on trait to show that the character is a bit 'different' or 'unconventional' in some way. That's how I felt about 13 in House, for example (but that could just be me) .