Disclaimer: Female lead doesn't have to be a bitch (though I'm okay with it if she is), but she does have to be rich.

Either her family is rich or she's a princess.

Kinda like Nogizaka Haruka no Himitsu, but without the legion of super maids.

Her and the male lead (regular joe) fall for each other.

Maybe there's a plot where she's in an arranged marriage or something. Maybe they are ripped apart like star crossed lovers, but still get together.

tenshi na konamaiki perfectly matches ur description

female : rich, arrogant, beautiful, talented, and fighter
male(s) : bunch of nobodies chasing and competing to win her heart

In most of these, the female leads are pretty nice, but they are wealthier/higher social class than the male leads. They are also shoujo. Most of them are historical.

Joou no Hana - A princess falls for her servant. Medieval China.
Palace Meidi - An empress falls in love with her attendant. Taisho era like setting.
Teruteru x Shounen - The female lead is rather arrogant in this one. The male lead is her bodyguard. This is the only one that's not historical.
Koi Tsukiyo no Himegoto - Wealthy girl and a student. Taisho era.
Ojousama no Untenshu - Wealthy girl and her chauffeur. Taisho era.

Versailles no Bara - This one is a tragedy, but it's a classic. Set in France during the revolution.