Where does this "often" happen? Why would any bi woman give a shit about whether her partner is attracted to trans people? The only thing that matters to the vast majority of couples is whether both partners are attracted to each other. No one goes out of their way to say "hey, you should ogle more people who aren't me".
You can mince words all you want, but having prejudiced beliefs about bisexuals is, in fact, the definition of biphobia. There's nothing stopping anyone from refusing to date someone because of that - hell, I'd encourage them to. There's nothing worse than thinking you love someone and then finding out they think you're a cheating slut who needs to be "fixed".