Bellatrix would hate her because Hermione is everything she has been brought up to hate, not to mention she's obnoxious and thinks she knows everything and is far too idealistic for her own good.
Hermione would hate her on principle, because Bella's a prejudiced bitch and is unapologetic for her vindictive and cruel streak.
And as crazy and cruel and honestly sociopathic as Bella is, there is no doubt she is also has an insanely sharp wit, and a keen understanding of people and how they think and how they work and she has perfected the art of pinpointing people's weaknesses and just ripping into them without restraint.
Like literally give her the most confident, self-assured, egotist you can find and she would have them on their knees crying in like five minutes.
Enter Hermione, stubborn and short-tempered, told her entire life she was less than everyone else, made to feel inadequate ever since she was a child, and there is nothing Bella can tell her that she hasn't already heard before.
Bella is simultaneously annoyed and intrigued, because while Hermione is exceptionally easy to anger, she is considerably harder to break
Bella gets this intense, kind of creepy, subtle obsession with Hermione Granger because oh my god Bella is nothing if not obsessive.
Hermione cannot for the life of her understand why Bella won't just leave her alone.
And it's Bella's ability to read into people is suddenly backfiring on her because the more time she spends picking Hermione's brain the more she likes her.
Because Hermione is everything she has been bred to hate, but she's so fascinating, and she's vicious, and the way her eyes flash when she's about to go off on some intellectual rant because of something she said has Bella higher than she's ever felt.
And it's not as if Bella has ever really listened that much to her family in the first place, they were never close, she never liked them, but she likes Hermione.
And Hermione, quite against her will, starts noticing positive attributes about Bella's personality. And its not as if she forgets all the horrible parts of Bellatrix's personality, its just that she's also noticing how observant she is, and intelligent, and her eyes when she smiles and oh my god her legs–
It's like Bella's not this one dimensional evil woman anymore, she's intelligent and witty and interesting and troubled and Hermione finds herself wishing she could just look at her and understand her the way Bella seems to do with everyone else.
And one day Bella makes some flirtatious comment–probably not even purposefully, it just sounds vaguely suggestive–and Hermione freaks and Bellatrix is just like yes.
And it just spirals, and Bella finds that the dirtier the flirtatious comment, the bigger the reaction she gets out of Hermione, and oh my god Bella is capable of the filthiest dirty-talk.
And suddenly their interactions lack the animosity of before, and it's still Bella picking at Hermione and Hermione lashing out but they aren't angry anymore, and they don't hate each other, and its almost as if their day isn't complete unless they have their tiff at some point.
It's subtle, because to everyone else nothing has changed, the two of them still hate each other and every time they're around each other everyone sort of braces themselves because there's never any stopping it, you just have to let it run its course.
And that's why when it happens, when they're suddenly a thing, its so shocking
literally no one understands.
Because they don't even like each other??? They only ever fight?? at any given moment Hermione looks as if she is literally just about to slice Bellatrix's throat open and honestly Bella's expression is no better?
But that's just the way they are, they throw insults and Hermione loses her temper and Bella loves seeing Hermione angry and Hermione loves putting Bellatrix in her place,
and you know Hermione is dominant in bed–out of the two of them, she is clearly the control freak, and as if she wouldn't pass up an opportunity to get back at Bella for being ridiculous–and oh my god Bella loves it.
Neither are big fans of PDA, especially Bella.
When they're alone, though, Bella is so much more affectionate.
It's sort of a different type of affection, its quiet, it's sliding her hand under the waistband of Hermione's shorts when her hand is around her waist just so she can feel her skin, it's threading their fingers together while they're in bed (it's sitting at her feet and spreading her knees sliding her hands up the inside of her thighs because goddamn it put your book down you read all the time pay attention to me–).
And Bella gets jealous. Of everyone. And she acts on her jealousy. With violence.
But Hermione isn't an idiot and 99% of the time she is able to intercept Bella's attempts to incapacitate anyone she perceives as a threat.
They never get comfortable with PDA, it's just not in the nature of their relationship, but oh my god they flirt and it is so jarring to everyone around them.
Hermione tries not to, honestly, it's just that Bella is very good at getting under her skin, she always has been.
So Bella will say something decidedly filthy and Hermione will threaten her with something horrendously sexual and everyone around them is just like 'oh my god please no I don't need to know all the kinky sex you two get up to oh god please stop'(Hermione is at least embarrassed if someone overhears. Bella is always just proud).
Basically just this ridiculous couple that everyone assumes hate each other but then you find out they live together and have a cat and it's so confusing because there is no way they are a couple clearly they hate each other.
But its there's no animosity when they're throwing insults, there's a strange sort of fondness instead, and the way their eyes seem to linger on the other as often as possible, as if the last thing they ever want to do is look away.
No one really gets it, but Hermione seems happy regardless, and Bellatrix is decidedly less of a problem in Hermione's hands.
So they let it be