Biography
Romantic relationships, sex, and romantic and sexual attraction are staples of fiction, and — unless you're dealing with asexual and aromantic characters or a No Hugging, No Kissing setting — characters will express at least some desire for it. The vast majority of the time, male characters are attracted to women, and female characters are attracted to men, there are some gay and lesbian characters, and very rarely you'll get a bisexual character (unless it's a Queer Romance, where naturally the last two categories are more common), but others aren't so definite. Sometimes there's a male/female character who doesn't express interest in women/men but does seems to show interest in people the same gender as they; they're Ambiguously Gay. Then there are characters that seemingly show romantic and/or sexual interest in people of multiple genders; they're Ambiguously Bi.
Most of the time, this character's interest in people of a different gender is explicitly stated or written to be obvious, while their interest in people of the same gender is subtle or downplayed, but the inverse does exist. Characters with a Heterosexual Life Partner are especially prone to this, as while they might have an actual love interest of a different gender or try to get a love interest through flirting and having crushes on women, the relationship with their HLP often has a romantic/sexual element as well. Getting Crap Past the Radar can be a reason for this trope, the writers wanting to include hints a character is gay or bi but with enough heterosexuality to appease the Moral Guardians.
It should be noted that what makes a character Ambiguously Bi and what differentiates them from Bisexual characters is largely a matter of opinion. The character does not have to officially be declared bi to qualify, and as No Bisexuals demonstrates, even if a character is clearly bisexual to the audience, much of the time the writers don’t consider it as a possibility. Obviously, some form of attraction to people of different genders is required, but the exact extent varies; for some people, an offhand comment or a prolonged glance can be enough; for others, nothing short of onscreen sex can suggest bisexuality as a possibility. Characters who express If It's You, It's Okay further muddle the issue, as by definition, that makes a character bisexual, but there are otherwise straight, gay, and lesbian people in real life who do have exceptions to the "rule" of their sexuality.
This can overlap with Word of Gay if the character's bisexuality remains ambiguous within the work itself, but is directly declared elsewhere by a creator.
Compare/contrast Ambiguously Gay, Ambiguous Gender Identity, Depraved Bisexual and Bi-Wildered. See also Pseudo-Romantic Friendship. A supertrope to Alcohol-Induced Bisexuality.