If someone has a desire for or the capability to enjoy sex with both males and females, they are neither heterosexual, nor homosexual. They also do not change their sexuality. They are simply bisexual. The fluidity here lies in whether someone has at some point in time more interest in women or men and which desire they act upon. If one's interest in one of the sexes goes to zero, then one could argue that persons sexuality did indeed change from bisexual to hetero- or homo-sexual.
Bisexuals indeed have the unique opportunity to "decide" which side of their sexuality they pursue, because they enjoy both. That's what makes them different from "true" heterosexuals and homosexuals who can not enjoy both. (Though one could argue a homosexual forcing himself to have sex with a woman and make a family is not truly homosexual and we do know that's possible and happened quite often. I will leave that to the philosophers.)
Please keep in mind I am not even arguing for the "born this way" view. I have a "It does not matter" stance. I welcome ideology free research to clear it up though, but don't we already know the results? Both genes and environment play a role...