Immortality Bisexuality

While characters with normal lifespans are usually depicted as being attracted to one gender exclusively, immortal characters often turn out to be much less picky about gender. This could be attributed to the fact that we can't know for sure how human sexuality acts over a lifespan of centuries, or a strong belief in the Kinsey Scale from the author. Mostly, this is rationalized with a belief that someone who has lived long enough can look outside the box of sexual norms, or that in that amount of time someone of an unexpected gender is bound to attract the character. Or maybe they've just been around for so long that they're running out of new things to try.

This trope does have some Unfortunate Implications however, in that it ignores the very real pattern of being attracted to one gender that is displayed by gay and straight people alike throughout their lives. Many an author also lumps it together with Immortality Immorality, feeding into the notion that bisexuality isn't a legitimate orientation as much as it is promiscuity.

Examples of Immortality Bisexuality include:

Anime and Manga

Depending on how one interprets the nature of the series, France, as well as many other cast members from Axis Powers Hetalia.
Rin from Mnemosyne. All immortals in that series are either bi or lesbian, presumably to avoid Mayfly-December Romance (since only women can become immortal).
Gemna from Ninja Scroll.

Comic Books

Possibly explains why all the Elf Quest elves (some immortal, some just very long-lived) are bisexual.
Chris Claremont originally intended to write Wolverine as bisexual, and although he may or may not be technically immortal, his Healing Factor definitely grants extended longevity and makes him hard to kill. Of course, at the time, fans of comic books were probably less likely to be able to grasp the idea of "a manly dude that swings both ways" and so that angle was dropped. We know better now, though.
- His son Daken seems to be less choosy about whom he seduces though.

Literature

Averted at least twice in the Dresden Files: in Blood Rites it's revealed that Lord Raith, the King of the White Court Vampires (who are essentially incubi and succubi and feed on lust rather than blood) keeps House Raith in order by sexually dominating his offspring in order to enforce psychic subservience. However, as Lord Raith is one of the few White Court vampires who isn't bisexual, he instead attempts to kill his male offspring in non-direct ways (since the White Court as a whole frowns on a lack of subtly in one's evil plots).
Orlando: A Biography by Virginia Woolf has an immortal man switch genders after a long period of slumber. Alan Moore's The League of Extraordinary Gentlemen turned the character into a full-fledged immortal bisexual.
In The Witcher books, one of the witches mentions that when you live that long you will try everything eventually.
One of the Light Others from Night Watch named Ignat is a master of seduction, and doesn't care about the gender of his targets. He's not quite immortal, but he and all other Others can maintain youth for up to centuries, and it's implied that his bisexuality is at least in part because he's bored. He's possibly the only bisexual Other shown, but a lot of them tend toward being The Hedonist.
- He also doesn't mind having a threesome with two sorceresses, one of whom has a boyfriend in the next room.
The Vampires—yes, all of them—in The Vampire Chronicles.
Henry Fitzroy from the Blood Books. Vaguely implied with another, female vampire that Vicki encounters in a short story.
A way of life in A Dirge for Prester John. Not to mention taking lovers from a number of different species.

Live-Action TV

Trill in Star Trek, especially Dax in Star Trek: Deep Space Nine. A Trill symbiant is passed down from host to host in either a male or female body, but the trill symbiosis commission forbids relations with a former lover. One episode Dax ignores this and kisses a woman who the symbiants in each of them were once married together, but all her other relations on the show were straight.
Jack Harkness from Doctor Who and Torchwood—though he was omnisexual long before he became immortal.

Jack: You people and your quaint little categories.

True Blood: Word of God says that almost EVERY vampire out there is bisexual, gender being only a footnote to them. This is in stark contrast to the book series True Blood is based on, The Sookie Stackhouse Mysteries, where bisexuality is rare, outside of the occasional off-handed "I was bored" comments.
Spike once said of Angel in Angel: "Angel and I were never intimate. Well, except that one time..."

Mythology

Zeus.

Tabletop Games

Changeling: The Dreaming. As the kithain's reincarnation process isn't exactly tied down by things like gender, star-crossed lovers tend to be flexible just in case.
In the New World of Darkness sourcebook Immortals, exactly one of the sample NPCs is off-handedly described as sleeping with both sexes. She is also a serial killer, although the book doesn't imply that her sexuality has been influenced by her immortality or that her frequent murders are a natural outgrowth of her sexuality.
The Exalted—if not everyone in Creation—are typically portrayed as this. The Dragon-Blooded often take homosexual lovers outside of marriage to avoid the risk of siring bastards, the Lunars have easy access to Gender Bender powers and massive fecundity, the Solars are god-kings who traverse Creation like a man walking down the block and occasionally go into states of utter debauchery, and the Sidereals live for millennia and have fate powers that allow them to assume any role they want.
In some Dungeons & Dragons supplements—those few that mention sex—elves are generally portrayed as being much more likely to be bisexual than humans and other "brief" races.

Video Games

Vamp from Metal Gear Solid.
The Asari from Mass Effect are a One-Gender Race (all female, in appearance, anyway) and can have children with any gender or species. They can live to be almost 1000. They do sometimes mate with their own species, but those who do are frowned upon by creating more pureblood asari, which led to the Ardat-Yakshi.
Reaver from Fable II.

Webcomics

The Drow (and presumably other Fae) of Drowtales are Type II immortals that live in an Everyone Is Bi society, with purely heterosexual and homosexual people existing as minorities.
Applies to at least the highblooded trolls of Homestuck. It's normal for all trolls to be bisexual; monosexuality does exist, but it's not common or considered to be a big deal (it's kind of similar to how we'd view someone who's only attracted to redheads: not typical, but not remarkable enough to have a word for it or much of a stigma attached to it). However, the trope doesn't apply to all trolls because the lowest castes have shorter natural lifespans than humans, and somewhat higher up the hierarchy are trolls with humanlike lifespans, and so forth.

Web Original

Sakiko on the forum roleplay Honorable Hogwarts. She's 2,800 years old and bisexual.
In Tales of MU elves commonly use homosexuality as a form of birth control.