The reason for this trope, in general, may partly arise from confusion surrounding the behavior of real life bisexuals, who do not, as a rule, date males and females simultaneously. In addition, most bisexuals prefer one sex over another at any one time and some will only occasionally date those who are the opposite of their stated sexual preference. They may even deny being bisexual if one were to directly ask them, and given the wide spectrum of human sexual behavior — and modern societal pressures — it would be difficult to tell a true bisexual from someone who's deliberately trying to hide their own sexual preference by dating members of the opposing sex. Furthermore, most people in general are monogamous, and will eventually settle down with someone (usually) of one sex or the other; some will inevitably conclude from this that the person in question "wasn't really bi after all".
This can have to do with the particular times. The late Rock Hudson was reportedly bisexual, and from some reports was more interested in men than women, although for obvious reasons the climate of the time (1960s and 1970s) would have ruined his career if this was known to the public. It would probably have been hard enough if he were reported as gay, or "turned" gay (this was a more-or-less open secret with Paul Lynde, but it still wasn't publicly stated he was gay until after he died). As being bisexual is considered by the general public as being "more weird" than being "merely" gay, this would probably have destroyed Hudson's career then. Today, the comic Andy Dick has publicly admitted he's bisexual, and apparently this has not hurt his career, although his career is mostly built around him being crazy. Megan Fox is also open about being bisexual and it really hasn't hurt her at all. But since Girl-on-Girl Is Hot, a woman who admits to bisexuality always looks hotter to the average male viewer, unlike a man who does the same. (Then again, Fox has already admitted to blatantly lying to the media to shield off her private life, which appears to be working out just fine thus far.)
Surprisingly this trope is actually in an effect, to an extent, within the LGBT community (despite the B standing for Bisexual). Many, many people initially come out as bi before identifying as homosexual. This has led to a widely held perception that, in most cases, bisexuals are just people who don't want to admit to themselves that they aren't really attracted to the opposite gender at all. This belief is probably compounded by that fact that a lot of bisexuals don't feel a need to hang out at LGBT events (and certainly don't need to move into a Gayborhood), so bi people tend to be underrepresented the community anyway.