There are two ways to go about this, one more inflammatory than the other.
- Option 1 - character notices someone of the same gender, experiments, identifies as bi, ultimately says that they were straight all along and get in a relationship with someone of the 'opposite' gender.
- Option 2 - character notices someone of the same gender, experiments, identifies as bi, ultimately says that they were gay all along and from then on out are only in relationships with people of the same gender.
I personally call Option 1 "The Experimenting Trope" and Option 2 "The Stepping-Stone Trope". These don't exactly have to play out as I put up there, but those are usually the main components. Surprise surprise, TET is viewed as much more offensive than TSST. Which, okay, you do get gay/lesbian representation, but you're still trampling over other marginalized sexualities to get to that place.
You see it on TV. For anyone who watched the early seasons of Glee, you got to see Kurt call bisexual people 'gay people with a foot in the closet'. There was a movie called Kissing Jessica Stein, which I've seen a lot of people say that Jessica was 'actually straight the whole time' when in reality nothing is said about her orientation.
Most importantly though, you see it in real life. Members of any gender suddenly wonder "are they going to go back to [other gender]? Do they really like me or is this a phase?" In a phenomenon that is Most Certainly Not Sexism, bisexual men tend to get criticized for being 'actually gay, why don't you say you're gay, just get out of the closet', while bisexual women tend to get criticized for being 'actually straight, you're just doing this for attention and to show off to your boyfriend' (what boyfriend?) A lot of the distrust in the monosexual community regarding bisexuality comes from the harmful stereotype that bisexuality is just a phase people go through.
And if you thought you were bi at one time, but have now realized you were gay/straight, that's great! I'm really happy for you. This is not a criticism towards you, but rather towards the fictional narratives that are spun and the negative connotations that they bring to bisexuality. However, if you use your own experience or a friend's experience as a justification to discriminate towards bisexuals, know this: not everyone is like you. You may have used bisexuality as a stepping-stone or an experimentation, and that's fine, but genuine bisexuals exist who aren't using bisexuality as anything other than how to describe themselves. You are no longer in the community, ergo you don't get to speak over bisexual voices on bisexual issues.
Ways stop the negativity that the 'bisexual phase' narrative brings is to add more mogai people into stories. Have many bi people, have gay people, have bi people who used to identify as gay, have gay people who used to bi, have so many different narratives that one doesn't take over as the 'genuine experience'.