Nanami Kiryuu from Revolutionary Girl Utena. In the manga, Nanami only appears in a photo, so Juri takes her place as Alpha Bitch.
Soukou No Strain adds Isabella to the list of characters that it kills off, but her even worse successor, Mariette, makes it through to the end of the series. Oddly, Lavinia, who is named after the Alpha Bitch of A Little Princess, is the furthest thing from being an Alpha Bitch herself, being head-over-heels for protagonist Sarah.
Subverted in Red Garden. One of the Student Council members constantly complained about how the protagonist was being treated with kid gloves for her constant absences and tardies, and is seen several times spying on her, as if for blackmail material...then, in an emotional scene, she reveals that she's been worried about the protagonist for a long time, and wanted to help her with whoever is hurting her.
Shiho Huit fills this role in the anime, playing tricks on Arika and the other Corals and looking down on them because of their status.
Tomoe Marguerite is a more traditional Alpha Bitch, with a young hanger-on named Miya whom she verbally and physically abuses when no one else is looking. She's even tried to kill Arika and her friends on a few occasions.
The show also has Queen Mashiro, a Royal Brat who isn't even a student at the academy, but will skirt her administrative duties and visit there just to mock and laugh at Arika whenever she does something wrong.
Motoko Minagawa from Fruits Basket, complete with an obsessive crush on Yuki Sohma and a Girl Posse that harasses Tohru after she goes to live with Yuki and Shigure. In the manga, however, Motoko actually gets character development and gives up on Yuki.
Mao, an anime-only character in Kekkaishi, was apparently created to serve as Alpha Bitch for leading girl Tokine in that she flaunts her wealth and makes catty comments about her. Subverted because Tokine isn't really affected by her snarky comments.
Fukiko "Miya-sama" Ichinomiya, whose minions include, oh, the entire snotty Sorority, is another example, though her bitchiness doesn't show until the later chapters. Just like Aya, Fukiko is WAY more bitchy in the manga than the anime.
Michiyo in Mahoraba acts like The Alpha Bitch Ojou to Asami out of insecurity. She really wants to be friends with Asami.
Ami of Toradora!, who usually hides her bitchiness behind a saccharine mask of sweetness until she feels she can get away with it. She does get Character Development, though, switching to Lovable Alpha Bitch. Being a very popular teen model, she's used to various people fawning over her and such. But, because she's a model, they expect her to be the cute, sunny, eternally bubbly girl she's often portrayed as. And she's sick of it.
Anna Maria from Blood+ is a poster girl for this trope, despite not having a very large part in the series. A Rich Bitch, her own posse of female followers, the teacher's pet, and being unreasonably rude and bullying. Naturally, she gets a slap to the face when Solomon invites Saya to dance instead of her.
Reiko Komori, one of Mamoru's friends in GaoGaiGar, seems to be a younger, nicer version of this. The claws only come out on Sunou, one of their other friends, to one-up him whenever he starts bragging.
Kurumi from Kimi ni Todoke gossips about, befriends, and manipulates the kindhearted and naive protagonist to get a boy to like her. Her comeuppance arrives when a comic relief P.E. teacher thinks Kurumi has the hots for him.
Otome Kato from School Days. Slightly subverted as she's a sports idol and not a Rich Bitch or cheerleader.
Naruto: when she was younger, Sakura was bullied by a trio of Alpha Bitches for her big forehead. Later, after they become rivals, Ino becomes something of an Alpha Bitch, but she soon grows out of it.
Mitsuko Souma from Battle Royale, though she's a bit more... shall we say, violent than is usually expected.
In Aim for the Ace!, the beautiful star player Reika Ryuuzaki starts out acting like this, being the queen bee and at first angered that a newcomer like Hiromi could possibly have made the top five, but she warms up to her eventually.
Queen Barby from Panty & Stocking with Garterbelt, who runs the school that Panty and Stocking are infiltrating in one episode (it's even explicitly stated that the weak-willed principal barely has any control compared to her). She turns out to be one of the Ghosts Panty and Stocking are after: a literal Queen Bee.
Hell Girl has a lot of these, at least in the beginning of the series. And they receive their comeuppance. Boy, do they ever.
The worst of them is Aya Kuroda from the anime's very first episode. She not only bullies her rival Mayumi Hashimoto, but she frames her for embezzlement, forces her into Compensated Dating to earn the money back, and blackmails her with photos of her "illegal/immoral behavior" Seeing her get Dragged Off to Hell is quite satisfying, even if Mayumi must also suffer the same fate when she dies.
Later, we meet Shiori Akasaka, who leaves her friend Minami and gets "chosen" to go to Hell, but later, they get reconciled and try to send their rival alpha bitches to Hell instead. That does NOT end well.
And later, it's subverted: young Maki is being bullied by a secret stalker... and it turns out to be her teacher Kamishiro. She ends up in Hell.
The Ganguro Girls from Durarara!!. While they're not rich (if episode 6 is anything to go by, they're dirt poor), they have all the traits of this character; they take delight in tormenting the female lead Anri Sonohara, are catty and rude to everyone they meet, and are all around nasty and unlikable people. Is it any wonder that the Slasher decided to target them?
Kitchen Princess The popular girl and model Akane Kishida falls under this trope because she constantly frames the Genki Girl heroine for things that weren't her fault. The Wounded Gazelle Gambit is one of her favorite cards to play, and her posse falls for it every time.
Kyo Koi O Hajimemasu: Arisa and her posse react very badly when they find out the main character has become the resident playboy's girlfriend, going so far as to physically assault and bully her. She later employs two thugs to scare Hibino, but, to her horror, they try to rape her. This shakes her, making her apologise.
In the manga version of Yu-Gi-Oh! GX, Seika Kohinata fills this role. Unlike most examples of this Trope, she has the skills to back up her ego. (In her one duel with Judai, she honestly wasn't bad.)
Kill la Kill features a whole SCHOOL of Alpha Bitches, the top one being the owner of the school, Satsuki Kiyujin. Hakote the tennis firing squad captain (110 Million Battery-And-Serve) and Nonon "Pomp-And-Circumstance 'em" Jakuzure the sonic wave symphony captain are some of the higher tiers. In an ironic twist, while they are genuinely alpha bitches, they're working for the greater good of stopping Satsuki's bitch-crazy mother from literally destroying the world. They get much better after revealing their intentions to save the world and not destroy it, which allows them to talk about their serious issues. Oh, and Harime Nui, Satsuki's also-crazy stepsister, plays the trope straight as a lone-wolf alpha bitch, constantly insulting / degrading the cast while blocking their Power Armor augmented attacks without wearing Power Armor(not that she needs it...) and acting like a Mary Sue. And Mako has her own episode where she slowly turns into an Alpha Bitch, but stops herself near the end.