mjhjmtu

I don't think you need to show anything special at all.

Lots of people have multiple love interests (or hookups) over the course of a novel. In some novels, it's entire the premise.

If a character's first relationship in the novel was to a tall blond German runner, you wouldn't think your readers would be confused when the next relationship is with a short bald Nigerian physics professor.

Let your reader be confused. Most readers will figure it out pretty quickly. The few that don't, well, they're the readers that wouldn't really get it after you explained it either.

So how can I believably and casually show that Eris swings both ways ...

EDITED: After clarification from the OP, my first example won't work; the protagonists are too young (~16). However, the answer is roughly the same:

Casually! Have a conversation between Eris and Caspian, or Eris and a friend. And (in the modern world), I'd put aside the "confusion", teenagers in a modern secular city understand same-sex attraction just fine.

An Example: At 16/17 I assume the characters are juniors in high school, eleventh grade in the USA. This would be set in a private conversation, although walking together outdoors is private enough. I put this after a first kiss; for modern times that might be on a first date. If this is the most intimate they've each been with another, that would justify their willingness to be open.

Caspian asked, "Have you ever kissed before? I mean, before me."

"No. Until I met you, my biggest crush was on Elly in the eighth grade. I had dreams about kissing that girl."

Caspian laughed. "Oh, wow. Well, we have that in common. Did you dream about me?"

"Yes. A lot. Have you kissed anybody? Before me?"

"You are my first. I mean besides dreams."

Eris laughed. "Well, it's hard for me to compete with dreams."

"Not so hard," Caspian said. "It's like if you never had ice cream and you keep dreaming about having ice cream, and then you really have ice cream, it's a million times better than you could imagine. I'll choose the real you any day."

Again, the conversation is casual romantic talk. Caspian is only casually surprised Eris admits to her biggest crush being on a girl, and Eris doesn't hesitate to reveal that fact.

The final sentence actually foreshadows the later triangle. Caspian means it in a romantic sense, but Eris has already revealed her dreams of hooking up with Elly, so applied to that, Caspian's assertion that reality can far exceed her dream of a same-sex relationship will, in some sense, come to pass. She will fall in love with Marina.

Is Eris aware of her bisexuality herself? Or is she maybe confused at first as well? If the latter is the case, I think it's quite simple - you can write about her feelings on the subject, and people will understand.

So it all depends a bit on how confident Eris is about her sexuality, and how dramatic the whole thing should be. But I'm going to assume that she herself is not confused by this and that it's not supposed to be a dramatic reveal with a hurt male ex-lover coming to terms with her bisexuality or anything like that, since you say it's supposed to be "casual". You also say that she's grown up isolated, so maybe she never even questioned her bisexual feelings anyway, because the mainstream society we know and love/hate has not influenced her on what is considered appropriate.

In that case, there are two solutions in my mind: the one proposed by Cyn - just don't mention it, people will get it - and the one where someone asks her about it, and she gets the chance for a casual statement. For example a best friend who sees her kissing Marina could ask her "Oh, I thought you were interested in men! What happened?", and she could reply, depending on her character, something like "Uh, bisexuality, it's a thing, google it", or "Actually I don't really have preferences, and Marina is hot as hell". Or whatever. But I don't think such a situation seems forced, because between friends it is perfectly fine to ask about each other's sexual preferences, and to give an honest answer.

I think both are valid, but Cyn's version of not saying anything would be a bit too "aggressively casual" for me personally, I would prefer that someone mentions it but that everyone is cool with it. In our society, LGBT is still something that stands out from the crowd - not in a negative way in many cases, but still in a way that people want to acknowledge it. Just like you would have people remarking on brightly colored hair, it's something that people like to talk about and are curious about.

If you truly want to be casual, don't mention it at all. Let the reader work it out for themselves.

But, be aware of erasing bi and trans identities, you aren't doing them any favors by "normalizing" to gay

You are setting up a love triangle which may or may not have a conclusion with one being picked over the other. Reader (and author) expectations are a Chekov's gun – no story stands independent of reality. If one person in the triangle is seen as the inevitable conclusion of the character's self-discovery, or coded as the healthier choice by reasons of plot/character, it adds all sorts of implications on the final outcome.

When you shift a character's sexual orientation, there are socially-coded "rules" that popular media seems to reenforce. You are "swimming against a current" of reader expectations, and the normal might depend on the culture.

Characters are rewarded for moving from "straight" to "gay".

Characters are punished for moving from "gay" to "straight".

One is seen as "true", the other is seen as "false". This is of course not how fluid sexuality works, and it completely ignores the experiences of bi and trans people who's normal sexual identities are erased under this "rule".

The rule reflects a modern convention that people will be happier once they "admit" they are gay and stop "pretending" to be straight to conform to society. And of course it use to be the Freudian opposite, gay people were unhappy until they conformed to straight. Both are a reflection of "Heteronormativity" (I won't make up a word like "queernormativity" but that is exactly the dynamic even though it's an oxymoron, it is a reaction to heteronormativity).

To preserve this idea a modern corollary to the rule is also enforced: people who were once "gay" and now have a "straight" relationship are in denial of their "true" selves, they are psychologically false or being deceptive for personal gain.

Again, this isn't how real fluid sexuality works, but this bias is very strongly re-enforced by a society that is uncomfortable with people they can't put in a permanent box, and stick a pin in so they won't squirm out. Be aware of the biases inherent in your generation and your immediate social group.

You are writing bi and trans characters, but are you representing them in a way that is true to their nature, or are you "normalizing" them to confirm social and sexual biases? The issue is that Bi and trans people are sub-minority even as they are lumped under LGBT, so they are erased twice. You may not have room to represent other bi or trans people in your story who could show there is no message behind the final relationship pairing.

If I'm reading correctly, the crux of your issue is this:

Eris is a girl, she forms a romantic attachment to a boy, the reader
assumes she's straight. Later, when she forms a romantic attachment to
a girl, the reader may have problems believing it.

If you were to set the issue of sexuality completely aside and approach this as you would any other potentially unbelievable situation in a novel, it may help.

The general consensus for making something, that is potentially unbelievable, believable, is all about set up. To make the later scene with the girl feel completely natural to the reader and not at all unexpected, you can use foreshadowing earlier in your novel.

This concept applies to anything that may jar a reader if it isn't correctly set-up beforehand.

The Shining is a good example:

Stephen King needs the reader to believe that Danny is exceptional and
resourceful enough to resist the supernatural forces at play in the
hotel, more so even than the adults, and help his mother escape.

He does it by hinting at it in earlier dialogue:

“I asked if your wife fully understood what you would be taking on
here. And there’s your son, of course.” He glanced down at the
application in front of him. “Daniel. Your wife isn’t a bit
intimidated by the idea?”

“Wendy is an extraordinary woman.”

“And your son is also extraordinary?”

Jack smiled, a big wide PR smile. “We like to think so, I suppose.
He’s quite self-reliant for a five-year-old.”

If you set up and foreshadow Eris's sexuality, subtly but deftly, in the lead up to the homosexual encounter (a glance here, a thought there, a quick comment in dialogue) it won't come a surprise to the reader and they will accept it without question.

Good luck!